Orbifold Euler characteristics of universal cotangent line bundles on ${\bar{M}}_{1,n}$

Abstract

A scheme of computing $χ(\mbar_{1,n}, L_1^{\otimes d_1}\otimes ... \otimes L_n^{\otimes d_n})$ is given. Here $\mbar_{1,n}$ is the moduli space of $n$-pointed stable curves of genus one and $L_i$ are the universal cotangent line bundles defined by $x_i^{\ast }({\omega }_{C/M})$, where $C \to \mbar_{1,n}$ is the universal curve, ${\omega }_{C/M}$ the relative dualizing sheaf and $x_i$ the marked point. This work is a sequel to \cite{YL1}.