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Mathematics > Algebraic Geometry

arXiv:1406.2299 (math)
[Submitted on 9 Jun 2014 (v1), last revised 14 Sep 2015 (this version, v3)]

Title:Fine compactified Jacobians of reduced curves

Authors:Margarida Melo, Antonio Rapagnetta, Filippo Viviani
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Abstract:To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian of X. We investigate the geometric properties of fine compactified Jacobians focusing on curves having locally planar singularities. We give examples of nodal curves admitting non isomorphic (and even non homeomorphic over the field of complex numbers) fine compactified Jacobians. We study universal fine compactified Jacobians, which are relative fine compactified Jacobians over the semiuniversal deformation space of the curve X. Finally, we investigate the existence of twisted Abel maps with values in suitable fine compactified Jacobians.
Comments: 45 pages; final version, to appear in Trans. Amer. Math. Soc
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1406.2299 [math.AG]
  (or arXiv:1406.2299v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1406.2299
Journal reference: Trans. Amer. Math. Soc. 369 (2017), no. 8, 5341--5402

Submission history

From: Filippo Viviani [view email]
[v1] Mon, 9 Jun 2014 19:51:32 UTC (63 KB)
[v2] Fri, 8 May 2015 03:54:26 UTC (69 KB)
[v3] Mon, 14 Sep 2015 12:32:25 UTC (73 KB)
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