论文标题
在属属$ 3 $曲线的位置，该曲线接纳了Meromororphic差异的零订单$ 6 $和订单的极$ 2 $
On the locus of genus $3$ curves that admit meromorphic differentials with a zero of order $6$ and a pole of order $2$
论文作者
论文摘要
本文的主要目的是计算$ \叠加{\ Mathcal {m}} _ 3 $的除数的类别，该类别是通过闭合$ω\ Mathcal {M} _3（6; -2）$获得的notemapful地图而获得的。这是使用端口公式和测试曲线理论完成的。为此，我们研究了第二类的杂态差异的座位，将这些基因座地图的尺寸计算为$ \ Mathcal {M} _g $，并解决了一些涉及低属差异的枚举问题。证明的关键工具是贝恩布里奇·奇德隆·格鲁休夫斯基·米勒最近引入的地层的压缩。
The main goal of this article is to compute the class of the divisor of $\overline{\mathcal{M}}_3$ obtained by taking the closure of the image of $Ω\mathcal{M}_3(6;-2)$ 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 $\mathcal{M}_g$ 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-Möller.
