Cohomology classes of strata of differentials

Sauvaget, Adrien¹

¹ Université Pierre et Marie Curie, Paris, France

Geometry & topology, Tome 23 (2019) no. 3, pp. 1085-1171.

Résumé

We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of multiplicities of zeros of the differential. The main goal of this paper is to compute the Poincaré-dual cohomology classes of all strata. We prove that all these classes are tautological and give an algorithm to compute them.

In the second part of the paper we study the Picard group of the strata. We use the tools introduced in the first part to deduce several relations in these Picard groups.

Détail

DOI : 10.2140/gt.2019.23.1085

Classification : 14C17, 14H10, 30F30, 32G15
Keywords: moduli spaces of curves, Hodge bundle, tautological classes, strata of differentials

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