2013
DOI: 10.48550/arxiv.1307.6614
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The Chow ring of the moduli space of curves of genus 6

Abstract: We determine the Chow ring (with Q-coefficients) of M 6 by showing that all Chow classes are tautological. In particular, all algebraic cohomology is tautological, and the natural map from Chow to cohomology is injective. To demonstrate the utility of these methods, we also give quick derivations of the Chow groups of moduli spaces of curves of lower genus. The genus 6 case relies on the particularly beautiful Brill-Noether theory in this case, and in particular on a rank 5 vector bundle "relativizing" a baby … Show more

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