关于ELSV公式的讲座
Lectures on the ELSV formula
摘要：
ELSV公式首先由Ekedahl、Lando、Shapiro和Vainshtein证明，将Hurwitz数与Hodge积分联系起来。Graber和Vakil利用射影直线的稳定映射的模空间的虚局部化给出了ELSV公式的另一种证明，并说明了如何利用射影直线相对于一点的相对稳定映射的模空间来简化其证明。在这篇文章中，我们解释了ELSV公式是什么，以及如何证明它的虚局部化的模空间相对稳定的地图，继Graber-Vakil。本文根据作者于2008年7月14- 20日在浙江大学数学科学中心暑期班“Teichmuller空间与曲线的模空间几何”的讲座而作。
英文摘要：
The ELSV formula, first proved by Ekedahl, Lando, Shapiro, and Vainshtein, relates Hurwitz numbers to Hodge integrals. Graber and Vakil gave another proof of the ELSV formula by virtual localization on moduli spaces of stable maps to the projective line, and also explained how to simplify their proof using moduli spaces of relative stable maps to the projective line relative to a point. In this expository article, we explain what the ELSV formula is and how to prove it by virtual localization on moduli spaces of relative stable maps, following Graber-Vakil. This note is based on lectures given by the author at Summer School on "Geometry of Teichmuller Spaces and Moduli Spaces of Curves" at Center of Mathematical Sciences, Zhejiang University, July 14--20, 2008.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
