Chen-Ruan cohomology of M1,n and M1,n

Abstract

In this work we compute the Chen-Ruan cohomology of the moduli spaces of smooth and stable n-pointed curves of genus 1. In the first part of the paper we study and describe stack theoretically the twisted sectors of M1,n and M1,n. In the second part, we study the orbifold intersection theory of M1,n. We suggest a definition for an orbifold tautological ring in genus 1, which is a subring of both the Chen-Ruan cohomology and of the stringy Chow ring. © Association des Annales de l'institut Fourier, 2013.