Cohomology classes of strata of differentials

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 a 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.

arXiv comment65 pages, 3 figures

References in corpus (8)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Hurwitz numbers and intersections on moduli spaces of curves
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• Double ramification cycles on the moduli spaces of curves
• Compactification of strata of abelian differentials
• Integrals of psi-classes over double ramification cycles
• The moduli space of twisted canonical divisors
• The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of $\Omega {\mathcal{M}}_g$

Cited by in corpus (5)

• Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
• Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials
• Infinitesimal structure of the pluricanonical double ramification locus
• Moduli spaces of residueless meromorphic differentials and the KP hierarchy
• Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails