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The Kodaira dimension of some moduli spaces of elliptic K3 surfaces

Mauro Fortuna, Giacomo Mezzedimi
<span title="2021-01-18">2021</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ntfj32dvonesdgjll5cwieq6yi" style="color: black;">Journal of the London Mathematical Society</a> </i> &nbsp;
We study the moduli spaces of elliptic K3 surfaces of Picard number at least 3, that is, U ⊕ −2k -polarized K3 surfaces. Such moduli spaces are proved to be of general type for k 220.  ...  Furthermore, explicit geometric constructions of some elliptic K3 surfaces lead to the unirationality of these moduli spaces for k < 11 and for 19 other isolated values up to k = 64.  ...  We would like to thank our PhD advisors Klaus Hulek and Matthias Schütt for many useful discussions and for reading an early draft of this manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1112/jlms.12430">doi:10.1112/jlms.12430</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ydcmuqyyujevdhnpiwfo2tz4oe">fatcat:ydcmuqyyujevdhnpiwfo2tz4oe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210716103144/https://londmathsoc.onlinelibrary.wiley.com/doi/pdfdirect/10.1112/jlms.12430" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fa/ff/faff4fbae7309a3ca04c59b2258516b3b5f54896.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1112/jlms.12430"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Lefschetz pencils and divisors in moduli space

Ivan Smith
<span title="2001-06-18">2001</span> <i title="Mathematical Sciences Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nk6cbwjm3re3xcnnbdd2g7hpyy" style="color: black;">Geometry and Topology</a> </i> &nbsp;
We study Lefschetz pencils on symplectic four-manifolds via the associated spheres in the moduli spaces of curves, and in particular their intersections with certain natural divisors.  ...  We also prove that only finitely many values of signature or Euler characteristic are realised by manifolds admitting Lefschetz pencils of genus two curves.  ...  Acknowledgements Thanks to Denis Auroux for comments on an earlier  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/gt.2001.5.579">doi:10.2140/gt.2001.5.579</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oc6bcfhvvnhdthw75vwqwsmk44">fatcat:oc6bcfhvvnhdthw75vwqwsmk44</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706143529/http://www.maths.soton.ac.uk/EMIS/journals/UW/gt/ftp/main/2001/2001-19.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2f/ff/2fffd9c4f68269640471d0b1b93a21a53d6fa844.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/gt.2001.5.579"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Compactified moduli spaces of rational curves in projective homogeneous varieties [article]

Kiryong Chung, Jaehyun Hong, Young-Hoon Kiem
<span title="2011-03-29">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The space of smooth rational curves of degree d in a projective variety X has compactifications by taking closures in the Hilbert scheme, the moduli space of stable sheaves or the moduli space of stable  ...  In this paper we compare these compactifications by explicit blow-ups and -downs when X is a projective homogeneous variety and d≤ 3.  ...  Deformations of morphisms and sheaves. Let Y be a projective curve with at worst nodal singularities and X be a smooth projective variety.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.0068v2">arXiv:1010.0068v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vq7mrmo3m5etvkzq2tk2lli2zi">fatcat:vq7mrmo3m5etvkzq2tk2lli2zi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171005094035/https://core.ac.uk/download/pdf/2149775.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/cc/a7cc2de3f3dc7978767bde6b6693e4e6a970b857.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.0068v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Recent results on the moduli spaces of Riemann surfaces

Kefeng Liu
<span title="">2005</span> <i title="International Press of Boston"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z2glhj6rfvawhmr2o4r3wonztm" style="color: black;">Surveys in Differential Geometry</a> </i> &nbsp;
A point in M g,h consists of (C, x 1 , . . . , x h ), a (nodal) curve and h smooth points on C.  ...  By adding stable nodal curves we get the projective Deligne-Mumford compactification M g , D = M g \ M g is a divisor of normal crossings. • Tangent and cotangent space: By the deformation theory of Kodaira-Spencer  ...  The proof of the geometric cut-and-join equation used Functorial Localization Formula: For ω ∈ H * T (X) an equivariant cohomology class, we have identity on F : This formula, similar to Riemann-Roch,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/sdg.2005.v10.n1.a3">doi:10.4310/sdg.2005.v10.n1.a3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/opf3nyryhnf6vclh4p46ffmkzi">fatcat:opf3nyryhnf6vclh4p46ffmkzi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809081454/http://www.cms.zju.edu.cn/UploadFiles/AttachFiles/200551883920249.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d8/e3/d8e33160b48210145b333f718c25eb45b6b091f3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/sdg.2005.v10.n1.a3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Birational geometry of the moduli space of quartic K3 surfaces [article]

Radu Laza, Kieran G. O'Grady
<span title="2016-07-05">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Specifically, in analogy with the so-called Hassett-Keel program for the moduli space of curves, we study the variation of log canonical models for locally symmetric varieties of Type IV associated to  ...  By work of Looijenga and others, one has a good understanding of the relationship between GIT and Baily-Borel compactifications for the moduli spaces of degree 2 K3 surfaces, cubic fourfolds, and a few  ...  By Riemann-Roch, both r and e are effective; it follows that r is the class of a rational curve which is the base-locus of ϕ L , and e is the class of the fiber of an elliptic fibration.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1607.01324v1">arXiv:1607.01324v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4wquymd6tvbnpn4lbmatzlq54i">fatcat:4wquymd6tvbnpn4lbmatzlq54i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200915040525/https://arxiv.org/pdf/1607.01324v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1f/56/1f56608dd54156cbecc6a378a076054fb5776835.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1607.01324v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Dawei Chen, Martin Möller
<span title="2012-12-31">2012</span> <i title="Mathematical Sciences Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nk6cbwjm3re3xcnnbdd2g7hpyy" style="color: black;">Geometry and Topology</a> </i> &nbsp;
This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.  ...  We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to  ...  The following geometric version of the Riemann-Roch theorem is useful for the study of canonical curves (see [ACGH85, p. 12 ] for more details). Theorem 2.4 (Geometric Riemann-Roch).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/gt.2012.16.2427">doi:10.2140/gt.2012.16.2427</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o2uzuvrri5gzze6r5sjg4evwzm">fatcat:o2uzuvrri5gzze6r5sjg4evwzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151016210305/https://www2.bc.edu/dawei-chen/sumlyap.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/23/77237fa493ff232c1708df777940bde9590d64ce.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/gt.2012.16.2427"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Non-varying sums of Lyapunov exponents of Abelian differentials in low genus [article]

Dawei Chen, Martin Moeller
<span title="2012-07-17">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This behavior is due to the disjointness property of Teichmueller curves with various geometrically defined divisors on moduli spaces of curves.  ...  We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmueller geodesic flow is the same for all Teichmueller curves in that stratum, hence equal  ...  The following geometric version of the Riemann-Roch theorem is useful for the study of canonical curves (see [ACGH85, p. 12 ] for more details). Theorem 2.4 (Geometric Riemann-Roch).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.3932v2">arXiv:1104.3932v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cljlgae3svgahm45zf3hir7ppy">fatcat:cljlgae3svgahm45zf3hir7ppy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1104.3932/1104.3932.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bc/be/bcbeae03216996bf436cc92e324c6da6b5a1b864.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.3932v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Infinitesimal deformations of nodal stable curves [article]

Scott A. Wolpert
<span title="2012-04-17">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The result generalizes the role of holomorphic quadratic differentials as cotangents for smooth curve families.  ...  Applications include an analytic description of the conormal sheaf for the locus of noded stable curves and a formula comparing infinitesimal openings of a node.  ...  We are interested in general curve families Π : C → B including nodal curves or equivalently analytic families of noded Riemann surfaces (possibly open) with smooth total space C and base B.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.3680v1">arXiv:1204.3680v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vcgvxvcnqnckvgzdpwtbi4ko5m">fatcat:vcgvxvcnqnckvgzdpwtbi4ko5m</a> </span>
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Moduli of sheaves supported on quartic space curves [article]

Jinwon Choi, Kiryong Chung, Mario Maican
<span title="2015-06-19">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The main idea of the proof is to relate the moduli space with the Hilbert scheme of curves by wall crossing.  ...  The moduli space has three irreducible components whose generic elements are, respectively, sheaves supported on rational quartic curves, on elliptic quartic curves, or on planar quartic curves.  ...  times along the exceptional divisors of blowing-ups of the stable maps space.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.1449v3">arXiv:1409.1449v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ro2yoglkrje7bjtlfss7pwbwvq">fatcat:ro2yoglkrje7bjtlfss7pwbwvq</a> </span>
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Lectures notes on compact Riemann surfaces [article]

Bertrand Eynard
<span title="2018-05-16">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
of solutions of algebraic equations. 2) Space of meromorphic functions and forms, we classify them with the Newton polygon. 3) Abel map, the Jacobian and Theta functions. 4) The Riemann--Roch theorem  ...  that computes the dimension of spaces of functions and forms with given orders of poles and zeros. 5) The moduli space of Riemann surfaces, with its combinatorial representation as Strebel graphs, and  ...  of finding a meromorphic section of a projective vector bundle whose fiber is a projective vector space (CP n ), over a compact Riemann surface Σ covering CP 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.06405v1">arXiv:1805.06405v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u7eojqpu4bdshn64skoxcedq5e">fatcat:u7eojqpu4bdshn64skoxcedq5e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191025005345/https://arxiv.org/pdf/1805.06405v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/50/ba/50ba2d79b2b7104f9477c459469eb6a8fccb3dcc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.06405v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Enumerative geometry via the moduli space of super Riemann surfaces [article]

Paul Norbury
<span title="2020-05-09">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces M_g,n.  ...  We give a new proof that a generating function for the intersection numbers of Θ_g,n with tautological classes on M_g,n is a KdV tau function.  ...  bundle over the moduli space of super Riemann surfaces.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.04378v1">arXiv:2005.04378v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ve7sc5ubvfdxignocqakjapoq">fatcat:5ve7sc5ubvfdxignocqakjapoq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200528191033/https://arxiv.org/pdf/2005.04378v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.04378v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The canonical ring of a stacky curve [article]

John Voight, David Zureick-Brown
<span title="2022-03-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As an application, we give an explicit presentation for graded rings of modular forms arising from finite-area quotients of the upper half-plane by Fuchsian groups.  ...  Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Gr\"obner basis.  ...  Classical case Let X be a (smooth projective) curve of genus g over a field k. A half-canonical divisor on X is a divisor L such that 2L = K is a canonical divisor.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.04657v4">arXiv:1501.04657v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jwtt2s4jtzb7fc2w6uqc7har3u">fatcat:jwtt2s4jtzb7fc2w6uqc7har3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200927072922/https://arxiv.org/pdf/1501.04657v3.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/87/83/87836ef5db3cf6c8440711dd757057b9d4fbb057.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.04657v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Cosmic String, Harvey-Moore Conjecture and Family Seiberg-Witten Theory [article]

Ai-Ko Liu
<span title="2004-09-02">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we study the enumeration of virtual numbers of immersed nodal curves along certain Calabi-Yau K3 fibrations.  ...  Based on the theory defining virtual numbers of nodal curves on algebraic surface (applying to a pencil of lattice polarized K3), a mathematical definition of virtual numbers of immersed rational curves  ...  The space M C−2 i≤l Ei contains the sub-moduli space which is the closure of the sub-space of irreducible smooth curves.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0409038v1">arXiv:math/0409038v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3n54gws4dfduliimifem7uqqri">fatcat:3n54gws4dfduliimifem7uqqri</a> </span>
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$D_5$ elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Mboyo Esole, James Fullwood, Shing-Tung Yau
<span title="">2015</span> <i title="International Press of Boston"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzbboalbq5c2npayrxtitv4kae" style="color: black;">Communications in Number Theory and Physics</a> </i> &nbsp;
We present for the first time Sen's (orientifold) limits for D 5 elliptic fibrations.  ...  We work over bases of arbitrary dimension and our results are independent of any Calabi-Yau hypothesis.  ...  Acknowledgements M.E. would like first to thank Anand Patel for his patient explanations of several algebraic geometry techniques related to the Grothendieck-Riemann-Rock theorem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/cntp.2015.v9.n3.a4">doi:10.4310/cntp.2015.v9.n3.a4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wv7sv2kufbgwteyvxd6d4mtwse">fatcat:wv7sv2kufbgwteyvxd6d4mtwse</a> </span>
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D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory [article]

Mboyo Esole, James Fullwood, Shing-Tung Yau
<span title="2011-10-27">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present for the first time Sen's (orientifold) limits for D5 elliptic fibrations.  ...  They provide simple examples of elliptic fibrations admitting a rich spectrum of singular fibers (not all on the list of Kodaira) without introducing singularities in the total space of the fibration and  ...  Acknowledgements M.E. would like first to thank Anand Patel for his patient explanations of several algebraic geometry techniques related to the Groethendieck-Riemann-Rock theorem.  ... 
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