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arXiv · 2402.19368

Orbifold Euler Characteristics of Compactified Jacobians

Sofia Wood
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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.

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Sofia Wood. 2024-02-29. Orbifold Euler Characteristics of Compactified Jacobians. https://doi.org/10.1017/s0305004125000180

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