The Chen-Ruan cohomology of moduli of curves of genus 2 with marked points

Mathematics – Algebraic Geometry

Scientific paper

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48 pages, 3 Figures. Final version to appear in Advances in Mathematics

Scientific paper

10.1016/j.aim.2011.12.017

In this work we describe the Chen-Ruan cohomology of the moduli stacks of smooth and stable genus 2 pointed curves, and its algebraic counterpart: the stringy Chow ring. In the first half of the paper we compute the additive structure of the Chen-Ruan cohomology ring for the moduli stack of stable pointed genus 2 curves, describing it as a rationally graded vector space. In the second part we give generators for the even Chen--Ruan cohomology ring as an algebra on the ordinary cohomology.

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