Degenerating the Jacobian: the Néron Model versus Stable Sheaves

Details Degenerating the Jacobian: the Néron Model versus Stable Sheaves Degenerating the Jacobian: the Néron Model versus Stable Sheaves

2010-12-12

arxiv.org/abs/1012.2576v2

Mathematics

Algebraic Geometry

23 pages. Revised with mostly expository changes

Scientific paper

A basic technique for studying a family of Jacobian varieties is to extend the family by adding degenerate fibers. Constructing an extension requires a choice of fibers, and one typically chooses to include either degenerate group varieties or degenerate moduli spaces of sheaves. Here we relate these two different approaches when the base of the family is a regular, 1-dimensional scheme such as a smooth curve. Specifically, we provide sufficient conditions for the line bundle locus in a family of compact moduli spaces of pure sheaves to be isomorphic to the N\'eron model. The result applies to moduli spaces constructed by Eduardo Esteves and Carlos Simpson, extending results of Busonero, Caporaso, Melo, Oda, Seshadri, and Viviani.

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