Euler characteristics of universal cotangent line bundles on $\mbar_{1,n}$

TL;DR

This paper presents an algorithm for computing Euler characteristics of line bundles on the moduli space of genus one curves with marked points, and provides a proof of a vanishing theorem for genus zero cases.

Contribution

It introduces an effective algorithm for Euler characteristic calculations on ar_{1,n} and offers a simple proof of Pandharipande's vanishing theorem for genus zero moduli spaces.

Findings

Algorithm for Euler characteristics on ar_{1,n}

Proof of Pandharipande's vanishing theorem for genus zero

Enhanced understanding of line bundle cohomology on moduli spaces

Abstract

We give an effective algorithm to compute the Euler characteristics $\chi(\mbar_{1,n}, \otimes_{i=1}^n L_i^{d_i})$. In addition, we give a simple proof of Pandharipande's vanishing theorem $H^j (\mbar_{0,n}, \otimes_{i=1}^n L_i^{d_i})=0$ for $j \ge 1, d_i \ge0$.