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

Abstract

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.

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

References in corpus (3)

• Generating stable modular graphs
• The orbifold cohomology of moduli of genus 3 curves
• The orbifold cohomology of moduli of hyperelliptic curves

Cited by in corpus (4)

• The structure of the tautological ring in genus one
• The orbifold cohomology of moduli of genus 3 curves
• Noncommutative rigidity of the moduli stack of stable pointed curves
• A formula for the total permutation-equivariant K-theoretic Gromov-Witten potential