Frederik Benirschke : Tautological classes of exact differentials

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

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April 24, 2023, 3 p.m.

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Abstract

One of the easiest ways of producing classes in the cohomology or Chow ring of the moduli space of curves is by taking the fundamental class of the hyperelliptic locus (or other loci of curves with rational functions of specified ramification). While we know that these classes are computable in theory by results of Faber-Pandharipande, no closed formulas are known in general. We explain a new approach using differential forms instead of rational functions. This allows to use the recent constructions of compactifications of moduli spaces of differentials by Bainbridge-Chen-Gendron-Grushevsky-Moeller. It turns out that, lifted to the moduli space of differentials, the classes are simply products of divisors.