Orbifold Euler Characteristics of Compactified Jacobians

Abstract

We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold Euler characteristic agrees with the Euler characteristic of the moduli space of stable, genus 0 curves with 2g+n markings up to a combinatorial factor, and in particular, is independent of the degree d and the choice of degree d universal fine compactified Jacobian. As a special case, we see that the universal fine compactified Jacobians defined by Kass and Pagani, depending on a universal polarization, have orbifold Euler characteristic independent of this choice of polarization.