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Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves [article]

Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2013 arXiv   pre-print
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves  ...  Furthermore, we identify the linear system with a plane curve that is shown to be rational and we develop algorithms to parametrize it analyzing its fields of parametrization.  ...  Application to the Approximate Parametrization Problem Given a non-rational irreducible curve, the approximate parametrization problem consists in providing a rational curve being at close Hausdorff distance  ... 
arXiv:1308.4466v1 fatcat:6yi74zk66ja2zb5c7ejnjdfgv4

Rational Hausdorff divisors: A new approach to the approximate parametrization of curves

Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2014 Journal of Computational and Applied Mathematics  
In this paper, we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves  ...  Approximate parametrization problem for plane curves: Given the implicit equation of a non-rational real plane curve C and a tolerance e > 0, decide whether there exists a rational real plane curve C at  ...  All authors belong to the Research Group ASYNACS (Ref. CCEE2011/R34).  ... 
doi:10.1016/j.cam.2013.12.052 fatcat:xgb2itfohrf5bm5htvknvamtzi

GW Invariants Relative Normal Crossings Divisors [article]

Eleny-Nicoleta Ionel
2014 arXiv   pre-print
In this paper we introduce a notion of symplectic normal crossings divisor V and define the GW invariant of a symplectic manifold X relative such a divisor.  ...  The main step is the construction of a compact moduli space of relatively stable maps into the pair (X, V) in the case V is a symplectic normal crossings divisor in X.  ...  ) identifying the new family of curves with the fibers of the universal curve.  ... 
arXiv:1103.3977v3 fatcat:htcacynyqba2tibkvnacpytj6u

GW invariants relative to normal crossing divisors

Eleny-Nicoleta Ionel
2015 Advances in Mathematics  
This will allow us to define the order of contact of J-holomorphic curves to V .  ...  (Donaldson divisors) Assume V is a normal crossing divisor in (X, ω, J), J is ωcompatible and [ω] has rational coefficients.  ...  ) identifying the new family of curves with the fibers of the universal curve.  ... 
doi:10.1016/j.aim.2015.04.027 fatcat:75et6d7pwvfz3mieeidcsyq3ym

Complete Calabi-Yau metrics in the complement of two divisors [article]

Tristan C. Collins, Yang Li
2022 arXiv   pre-print
We construct new complete Calabi-Yau metrics on the complement of an anticanonical divisors D in a Fano manifold of dimension at least three, when D consists of two transversely intersecting smooth divisors  ...  The asymptotic geometry is modeled on a generalization of the Calabi ansatz, related to the non-archimedean Monge-Ampère equation.  ...  We can thus glue the Calabi ansatz to the Tian-Yau metric, in a parametrized fashion over the x 1 variable, in order to achieve the partial completion of the generalized Calabi ansatz.  ... 
arXiv:2203.10656v1 fatcat:hr4t42fuezcaxdjtcruruxelcu

On the moduli of Kahler-Einstein Fano manifolds [article]

Yuji Odaka
2014 arXiv   pre-print
We also discuss the limits as Q-Fano varieties which should be put on the boundary of its canonical compactification.  ...  We prove that Kahler-Einstein Fano manifolds with finite automorphism groups form Hausdorff moduli algebraic space with only quotient singularities.  ...  The author appreciates the organizers of the Kinosaki symposium 2013, S. Kuroda, K. Yamada, K. Yoshioka, for inviting him to give the opportunity. The author would like to thank Professor S.  ... 
arXiv:1211.4833v4 fatcat:fxlkq6bsbzccvni3zez3ld3nnu

Approximate parametrization of plane algebraic curves by linear systems of curves

Sonia Pérez-Díaz, J. Rafael Sendra, Sonia L. Rueda, Juana Sendra
2010 Computer Aided Geometric Design  
The algorithm outputs a rational parametrization of a rational curve C of degree d which has the same points at infinity as C.  ...  In this paper, given a tolerance e > 0 and an e -irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of e -rationality, and we provide an algorithm to parametrize approximately  ...  a rational parametrization V(t) of a curve C  ... 
doi:10.1016/j.cagd.2009.12.002 fatcat:q6iwmfnanvfitpldhcpafd7ody

Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures [article]

Yuji Odaka
2020 arXiv   pre-print
For any degenerating Calabi-Yau family, we introduce new limit space which we call galaxy, whose dense subspace is the disjoint union of countably infinite open Calabi-Yau varieties, parametrized by the  ...  rational points of the Kontsevich-Soibelman's essential skeleton, while dominated by the Huber adification over the Puiseux series field.  ...  to the Calabi-Yau varieties in concern, to make natural logarithmic generalization (i.e., with boundary divisors) of the KSBA approach work.  ... 
arXiv:2011.12748v1 fatcat:pnl2iiysrfeothhrta3ogcuvvi

Tropical Geometric Compactification of Moduli, II - A_g case and holomorphic limits - [article]

Yuji Odaka
2017 arXiv   pre-print
We also do it for algebraic curves case and observe a crucial difference with the case of abelian varieties.  ...  This work is analogous to the first of our series (available at arXiv:1406.7772v2), which compactified the moduli of curves by attaching the moduli of metrized graphs.  ...  The original version of this preprint was e-print  ... 
arXiv:1705.05545v1 fatcat:vhnhl6hag5dcjbop5racbkbu6e

Algebraic and Analytic Compactifications of Moduli Spaces

Patricio Gallardo, Matt Kerr
2022 Notices of the American Mathematical Society  
The basic objects of algebraic geometry, such as subvarieties of a projective space, are defined by polynomial equations.  ...  The seemingly innocuous observation that one can vary the coefficients of these equations leads at once to unexpectedly deep questions: • When are objects with distinct coefficients equivalent?  ...  Each divisor parametrizes a different type of stable curve; e.g., the divisor 𝐷 12 generically parametrizes the union of two ℙ 1 s with the points distributed as in Fig. 3 .  ... 
doi:10.1090/noti2541 fatcat:enozzgjsiregnkjoi3pdtr4kkq

Nonuniformisable Foliations on Compact Complex Surfaces

M. Brunella
2009 Moscow Mathematical Journal  
We give a complete classification of holomorphic foliations on compact complex surfaces which are not uniformisable, i.e., for which universal coverings of the leaves do not glue together in a Hausdorff  ...  This leads to complex analogs of the Reeb component defined on certain Hopf surfaces and certain Kato surfaces.  ...  to a tree of rational curves.  ... 
doi:10.17323/1609-4514-2009-9-4-729-748 fatcat:c27kfcjx4vfu7ivt4pvxqfurze

Intersection of almost complex submanifolds [article]

Weiyi Zhang
2017 arXiv   pre-print
We show the intersection of a compact almost complex subvariety of dimension 4 and a compact almost complex submanifold of codimension 2 is a J-holomorphic curve.  ...  As an application, we discuss pseudoholomorphic sections of a complex line bundle. We introduce a method to produce J-holomorphic curves using the differential geometry of almost Hermitian manifolds.  ...  Since an exceptional curve of the first kind is obtained from consecutive blowups, the cohomology class of the corresponding pseudoholomorphic subvariety is a −1-rational curve class E 1 .  ... 
arXiv:1707.08253v1 fatcat:7lu47qfkzndh5ijlzb75lxb7ta

Intersection of almost complex submanifolds

Weiyi Zhang
2018 Cambridge Journal of Mathematics  
For a given almost Hermitian connection ∇ on Λ − J , all the pseudoholomorphic sections of the bundle Λ − J with the same zero divisor are linearly parametrized by C. Proof.  ...  This is a generalization of positivity of intersections for J-holomorphic curves in almost complex 4-manifolds to higher dimensions.  ...  suggestions to improve the presentation of this paper.  ... 
doi:10.4310/cjm.2018.v6.n4.a2 fatcat:sr4t2fww7zck7ap7hyctebypsu

Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum [article]

Nguyen-Bac Dang, Rostislav Grigorchuk, Mikhail Lyubich
2021 arXiv   pre-print
us to a notion of a spectral current).  ...  We show that the spectra in question can be interpreted as asymptotic distributions of slices by a line of iterated pullbacks of certain algebraic curves under the corresponding rational maps (leading  ...  Then the rational map R is rationally semi-conjugate to a degree d rational map on a curve. Theorem C produces a particular semi-conjugacy whose fibers are rational curves.  ... 
arXiv:2010.00675v2 fatcat:bo5thl2p4fbcdlcfxdoaeota5u

Abstracts of papers

1933 Bulletin of the American Mathematical Society  
Let f(z) be a function analytic in the interior of the unit circle of the s-plane Suppose that /(0)=0, and that there is an arc A on \z\ =1 such that when {z} is a sequence of points in \z\ <1 approaching  ...  Cross-references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of the abstract.  ...  The Mayer problem is treated both in parametric and in non-parametric form.  ... 
doi:10.1090/s0002-9904-1933-05581-7 fatcat:u4nnix2lv5ge3bqg74wwhr2ogi
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