Geometry & Topology

Cohomology classes of strata of differentials

Adrien Sauvaget

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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.

Article information

Source
Geom. Topol., Volume 23, Number 3 (2019), 1085-1171.

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1559700271

Digital Object Identifier
doi:10.2140/gt.2019.23.1085

Mathematical Reviews number (MathSciNet)
MR3956890

Zentralblatt MATH identifier
07079056

Subjects
Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14H10: Families, moduli (algebraic) 30F30: Differentials on Riemann surfaces 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]

Keywords
moduli spaces of curves Hodge bundle tautological classes strata of differentials

Citation

Sauvaget, Adrien. Cohomology classes of strata of differentials. Geom. Topol. 23 (2019), no. 3, 1085--1171. doi:10.2140/gt.2019.23.1085. https://projecteuclid.org/euclid.gt/1559700271


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