Cohomology of moduli spaces of genus 2 curves and the Gorenstein conjecture
The tautological ring plays a key role in the study of the the geometry of moduli spaces of curves. For a long time it had been expected that 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 M2,20. We use this to prove that the Gorenstein conjecture does not hold for these spaces. This is joint work with Dan Petersen.