Boundary expression for Chern classes of the Hodge bundle on spaces of cyclic covers
Boundary expression for Chern classes of the Hodge bundle on spaces of cyclic covers
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循环覆盖空间上霍奇丛陈氏类的边界表达式
DOI：
10.2140/involve.2021.14.571
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Seamus Somerstep
中科院分区：
文献类型：
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作者：
Bryson Owens;Seamus Somerstep
我们在 $n$ 点有理稳定曲线的可接受循环 $\mathbb{Z}/3\mathbb{Z}$ 覆盖空间上计算霍奇丛的第一陈类的显式公式，作为边界层的线性组合。然后我们应用这个公式给出一个递归公式来计算包含 $\lambda_1$ 的某些 Hodge 积分。我们还考虑使用 ${\mathbb{Z}}/{2\mathbb{Z}}$ 动作进行覆盖，我们将 $\lambda_2$ 计算为余维两个边界层的线性组合。
We compute an explicit formula for the first Chern class of the Hodge Bundle over the space of admissible cyclic $\mathbb{Z}/3\mathbb{Z}$ covers of $n$-pointed rational stable curves as a linear combination of boundary strata. We then apply this formula to give a recursive formula for calculating certain Hodge integrals containing $\lambda_1$. We also consider covers with a ${\mathbb{Z}}/{2\mathbb{Z}}$ action for which we compute $\lambda_2$ as a linear combination of codimension two boundary strata.