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Cohomology of moduli spaces of genus 2 curves and the Gorenstein conjecture

Orsola Tommasi
Leibniz Universitaet Hannover
Wednesday, March 5, 2014 - 11:30 to 13:00

A main theme in the study of the cohomology of moduli spaces of curves is the study of the tautological ring, a subring generated by certain geometrically natural classes. An open question is whether the tautological ring is a Gorenstein ring, as conjectured by Carel Faber in the case of smooth curves without marked points. In this talk we discuss an approach that allows to detect the existence of non-tautological classes in the cohomology ring of the moduli space of stable curves of genus 2 with sufficiently many marked points, such as those constructed by Graber and Pandharipande for \bar M_{2,20}. We use this to prove that the Gorenstein conjecture does not hold for these spaces. This is joint work with Dan Petersen (ETH Zuerich).

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