Geodesic
The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials
Forum of Mathematics, Pi, Tome 10 (2022)

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
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     title = {The {Chern} classes and {Euler} characteristic of the moduli spaces of {Abelian} differentials},
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Matteo Costantini; Martin Möller; Jonathan Zachhuber. The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials. Forum of Mathematics, Pi, Tome 10 (2022). doi: 10.1017/fmp.2022.10

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