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

2020/06/23 by Matteo Costantini, Martin Möller, Costantini, Matteo +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2006.12803

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.

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• Isoresidual fibrations and the birational geometry of moduli of pointed stable curves

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