线性超椭圆Hodge积分

Pub Date : 2023-11-27 DOI:10.1007/s00229-023-01519-x

Adam Afandi

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引用次数: 3

摘要

给出了超椭圆轨迹上的线性Hodge积分的一个封闭表达式。具体地说，我们找到了一个简洁的组合公式，用于在一个\(\lambda \) -类的超椭圆轨迹上的所有交点数，以及一个\(\psi \) -类的幂沿着分支映射向后拉。这是通过在一堆稳定的轨道图\(\left[ {\mathbb {P}}^1/{\mathbb {Z}}_2\right] \)上使用阿蒂亚-博特定位来实现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Linear hyperelliptic Hodge integrals

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Linear hyperelliptic Hodge integrals

We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one \(\lambda \)-class, and powers of a \(\psi \)-class pulled back along the branch map. This is achieved by using Atiyah–Bott localization on a stack of stable maps into the orbifold \(\left[ {\mathbb {P}}^1/{\mathbb {Z}}_2\right] \).

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