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arXiv · 1707.02284

The stability space of compactified universal Jacobians

Jesse Leo Kass·Nicola Pagani
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Abstract

In this paper we describe compactified universal Jacobians, i.e. compactifications of the moduli space of line bundles on smooth curves obtained as moduli spaces of rank 1 torsion-free sheaves on stable curves, using an approach due to Oda-Seshadri. We focus on the combinatorics of the stability conditions used to define compactified universal Jacobians. We explicitly describe an affine space, the stability space, with a decomposition into polytopes such that each polytope corresponds to a proper Deligne-Mumford stack that compactifies the moduli space of line bundles. We apply this description to describe the set of isomorphism classes of compactified universal Jacobians (answering a question of Melo), and to resolve the indeterminacy of the Abel-Jacobi sections (addressing a problem raised by Grushevsky-Zakharov).

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Jesse Leo Kass, Nicola Pagani. 2017-07-07. The stability space of compactified universal Jacobians. https://doi.org/10.1090/tran%2F7724

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