✦ LIBER ✦

Fine compactified Jacobians

✍ Scribed by Margarida Melo; Filippo Viviani

Publisher: John Wiley and Sons
Year: 2012
Tongue: English
Weight: 447 KB
Volume: 285
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.201100021

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✦ Synopsis

Abstract

We study Esteves's fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a one‐parameter regular local smoothing of a nodal curve X, the relative smooth locus of a relative fine compactified Jacobian is isomorphic to the Néron model of the Jacobian of the general fiber, and thus it provides a modular compactification of it. We show that each fine compactified Jacobian of X admits a stratification in terms of certain fine compactified Jacobians of partial normalizations of X and, moreover, that it can be realized as a quotient of the smooth locus of a suitable fine compactified Jacobian of the total blowup of X. Finally, we determine when a fine compactified Jacobian is isomorphic to the corresponding Oda‐Seshadri's coarse compactified Jacobian.

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