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2019 Cohomology classes of strata of differentials
Adrien Sauvaget
Geom. Topol. 23(3): 1085-1171 (2019). DOI: 10.2140/gt.2019.23.1085

Abstract

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.

Citation

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Adrien Sauvaget. "Cohomology classes of strata of differentials." Geom. Topol. 23 (3) 1085 - 1171, 2019. https://doi.org/10.2140/gt.2019.23.1085

Information

Received: 28 February 2017; Revised: 7 August 2018; Accepted: 18 September 2018; Published: 2019
First available in Project Euclid: 5 June 2019

zbMATH: 07079056
MathSciNet: MR3956890
Digital Object Identifier: 10.2140/gt.2019.23.1085

Subjects:
Primary: 14C17, 14H10, 30F30, 32G15

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.23 • No. 3 • 2019
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