Volume 23, issue 3 (2019)

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Cohomology classes of strata of differentials

Adrien Sauvaget

Geometry & Topology 23 (2019) 1085–1171

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.

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moduli spaces of curves, Hodge bundle, tautological classes, strata of differentials
Mathematical Subject Classification 2010
Primary: 14C17, 14H10, 30F30, 32G15
Received: 28 February 2017
Revised: 7 August 2018
Accepted: 18 September 2018
Published: 28 May 2019
Proposed: Jim Bryan
Seconded: Dan Abramovich, Anna Wienhard
Adrien Sauvaget
Université Pierre et Marie Curie