The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials
Matteo Costantini, Martin Möller, Jonathan Zachhuber
Abstract
Abstract For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most 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 multi-scale differentials and computational tools in the Chow ring, such as a description of normal bundles to boundary divisors.
Topics & Concepts
MathematicsCompactification (mathematics)Abelian groupModuli spacePure mathematicsCotangent bundleEuler characteristicEuler's formulaVector bundleMathematical analysisTrigonometric functionsGeometryMathematical Dynamics and FractalsHomotopy and Cohomology in Algebraic TopologyAlgebraic Geometry and Number Theory