The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials
Algebraic Geometry
2020-06-24 v1 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.2006.12803,
title = {The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials},
author = {Matteo Costantini and Martin Möller and Jonathan Zachhuber},
journal= {arXiv preprint arXiv:2006.12803},
year = {2020}
}
Comments
59 pages, 5 figures