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Cohomology classes of
strata of differentials
Adrien Sauvaget |
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Geometry & Topology 23 (2019) 1085–1171
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Abstract |
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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. |
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Keywords
moduli spaces of curves, Hodge bundle, tautological
classes, strata of differentials
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Mathematical Subject Classification 2010
Primary: 14C17, 14H10, 30F30, 32G15
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References |
Publication
Received: 28 February 2017
Revised: 7 August 2018
Accepted: 18 September 2018
Published: 28 May 2019
Proposed: Jim Bryan
Seconded: Dan Abramovich, Anna Wienhard
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Authors |
| Adrien Sauvaget | |
| Université Pierre et Marie
Curie Paris France |
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