The stability space of compactified universal Jacobians

Pagani, NT and Kass, JL (2019) The stability space of compactified universal Jacobians. Transactions of the American Mathematical Society, 372 (7). pp. 4851-4887.

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Official URL: https://www.ams.org/journals/tran/2019-372-07/S000...

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).

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	04 Dec 2018 09:45
Last Modified:	19 Jan 2023 01:11
DOI:	10.1090/tran/7724
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029209