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Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients

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arxiv 2303.17929 v2 pith:WMQCJB7P submitted 2023-03-31 math.AG

Matteo Costantini , Martin Möller , Johannes Schwab This is my paper · ORCID
classification math.AG
keywords spacesk-differentialsmoduliapplicationchernclasseslinearquotients
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We provide formulas for the Chern classes of linear submanifolds of the moduli spaces of Abelian differentials and hence for their Euler characteristic. This includes as special case the moduli spaces of k-differentials, for which we set up the full intersection theory package and implement it in the sage-program diffstrata. As an application, we give an algebraic proof of the theorems of Deligne-Mostow and Thurston that suitable compactifications of moduli spaces of k-differentials on the 5-punctured projective line with weights satisfying the INT-condition are quotients of the complex two-ball.

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