ON THE LOCUS OF GENUS 3 CURVES THAT ADMIT MEROMORPHIC DIFFERENTIALS WITH A ZERO OF ORDER 6 AND A POLE OF ORDER 2

被引：0

作者：

Castorena, Abel ^{[1
]}

Gendron, Quentin ^{[1
,2
]}

机构：

[1] Ctr Ciencias Matemat UNAM, Antigua Car Patzcuaro 8701, Morelia, Michoacan, Mexico

[2] Ctr Invest Matemat, AP 402, Guanjuato 36000, Gto, Mexico

来源：

ANNALES DE L INSTITUT FOURIER | 2022年 / 72卷 / 01期

关键词：

Abelian differentials; Differentials of second kind; Moduli Space of curves; Deligne-Mumford compactification; Picard group; MODULI SPACE; ABELIAN DIFFERENTIALS; KODAIRA DIMENSION; STRATA;

D O I：

10.5802/aif.3472

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main goal of this article is to compute the class of the divisor of (M) over bar3 obtained by taking the closure of the image of Omega M-3(6;-2) by the forgetful map. This is done using Porteous formula and the theory of test curves. For this purpose, we study the locus of meromorphic differentials of the second kind, computing the dimension of the map of these loci to M-g and solving some enumerative problems involving such differentials in low genus. A key tool of the proof is the compactification of strata recently introduced by Bainbridge-Chen-Gendron-Grushevsky-Moller.

引用

页码：261 / 299

页数：40

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