Geometry & Topology

Cohomology classes of strata of differentials

Adrien Sauvaget

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

moduli spaces of curves Hodge bundle tautological classes strata of differentials


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

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