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

2013
*
arXiv
*
pre-print

In this paper we introduce

arXiv:1308.4466v1
fatcat:6yi74zk66ja2zb5c7ejnjdfgv4
*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 ...##
###
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves

2014
*
Journal of Computational and Applied Mathematics
*

In this paper, we introduce

doi:10.1016/j.cam.2013.12.052
fatcat:xgb2itfohrf5bm5htvknvamtzi
*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). ...##
###
GW Invariants Relative Normal Crossings Divisors
[article]

2014
*
arXiv
*
pre-print

In this paper we introduce

arXiv:1103.3977v3
fatcat:htcacynyqba2tibkvnacpytj6u
*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*. ...##
###
GW invariants relative to normal crossing divisors

2015
*
Advances in Mathematics
*

This will allow us

doi:10.1016/j.aim.2015.04.027
fatcat:75et6d7pwvfz3mieeidcsyq3ym
*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*. ...##
###
Complete Calabi-Yau metrics in the complement of two divisors
[article]

2022
*
arXiv
*
pre-print

We construct

arXiv:2203.10656v1
fatcat:hr4t42fuezcaxdjtcruruxelcu
*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. ...##
###
On the moduli of Kahler-Einstein Fano manifolds
[article]

2014
*
arXiv
*
pre-print

We also discuss

arXiv:1211.4833v4
fatcat:fxlkq6bsbzccvni3zez3ld3nnu
*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. ...##
###
Approximate parametrization of plane algebraic curves by linear systems of curves

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 ...

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

2020
*
arXiv
*
pre-print

For any degenerating Calabi-Yau family, we introduce

arXiv:2011.12748v1
fatcat:pnl2iiysrfeothhrta3ogcuvvi
*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. ...##
###
Tropical Geometric Compactification of Moduli, II - A_g case and holomorphic limits -
[article]

2017
*
arXiv
*
pre-print

We also do it for algebraic

arXiv:1705.05545v1
fatcat:vhnhl6hag5dcjbop5racbkbu6e
*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 ...##
###
Algebraic and Analytic Compactifications of Moduli Spaces

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 . ...

##
###
Nonuniformisable Foliations on Compact Complex Surfaces

2009
*
Moscow Mathematical Journal
*

We give

doi:10.17323/1609-4514-2009-9-4-729-748
fatcat:c27kfcjx4vfu7ivt4pvxqfurze
*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*. ...##
###
Intersection of almost complex submanifolds
[article]

2017
*
arXiv
*
pre-print

We show

arXiv:1707.08253v1
fatcat:7lu47qfkzndh5ijlzb75lxb7ta
*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 . ...##
###
Intersection of almost complex submanifolds

2018
*
Cambridge Journal of Mathematics
*

For

doi:10.4310/cjm.2018.v6.n4.a2
fatcat:sr4t2fww7zck7ap7hyctebypsu
*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. ...##
###
Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum
[article]

2021
*
arXiv
*
pre-print

us

arXiv:2010.00675v2
fatcat:bo5thl2p4fbcdlcfxdoaeota5u
*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*. ...##
###
Abstracts of papers

1933
*
Bulletin of the American Mathematical Society
*

Let f(z) be

doi:10.1090/s0002-9904-1933-05581-7
fatcat:u4nnix2lv5ge3bqg74wwhr2ogi
*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. ...
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