Simpson Jacobians of reducible curves

2004/10/18 by Ana Cristina Lopez, Lopez, Ana Cristina
Mathematics · #14D20 #14D22 #14F05 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D20 #msc:14D22 #msc:14F05 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0410393

Latex file with 13 figures. Final version to appear in J. Reine. Angew. Math

arxiv created 2004/10/18 · arxiv updated 2009/12/01

Abstract

For any projective curve X let M^d(X) be the Simpson moduli space of pure dimension one rank 1 degree d sheaves that are semistable with respect to a fixed polarization H on X. When X is a reduced curve the connected component of M^d(X) that contains semistable line bundles can be considered as the compactified Jacobian of X. In this paper we give explicitly the structure of this compactified Simpson Jacobian for the following projective curves: tree-like curves and all reduced and reducible curves that can appear as Kodaira singular fibers of an elliptic fibration, that is, the fibers of types III, IV and I_N with N≥ 2

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