The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials

Autor:	Costantini, Matteo, Möller, Martin, Zachhuber, Jonathan
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth compactification by multi-scale differentials. It is a consequence of a formula for the full Chern polynomial of the cotangent bundle of the compactification. The main new technical tools are an Euler sequence for the cotangent bundle of the moduli space of Abelian differentials and computational tools in the Chow ring, such as normal bundles to boundary divisors. Comment: 59 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.12803 Zobrazit plný text záznamu View this record from Arxiv