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Mathematics > Algebraic Geometry

arXiv:1804.08481 (math)
[Submitted on 23 Apr 2018 (v1), last revised 12 Feb 2020 (this version, v3)]

Title:The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves

Authors:Andrea T. Ricolfi
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Abstract:Let $C$ be a hyperelliptic curve embedded in its Jacobian $J$ via an Abel-Jacobi map. We compute the scheme structure of the Hilbert scheme component of $\textrm{Hilb}_J$ containing the Abel-Jacobi curve as a point. We relate the result to the ramification (and to the fibres) of the Torelli morphism $\mathcal M_g\rightarrow \mathcal A_g$ along the hyperelliptic locus. As an application, we determine the scheme structure of the moduli space of Picard sheaves (introduced by Mukai) on a hyperelliptic Jacobian.
Comments: Improved the exposition according to the referees' suggestions. To appear in Algebra and Number Theory
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1804.08481 [math.AG]
  (or arXiv:1804.08481v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1804.08481
Journal reference: Alg. Number Th. 14 (2020) 1381-1397
Related DOI: https://doi.org/10.2140/ant.2020.14.1381

Submission history

From: Andrea T. Ricolfi [view email]
[v1] Mon, 23 Apr 2018 14:54:11 UTC (127 KB)
[v2] Fri, 10 Aug 2018 08:34:23 UTC (17 KB)
[v3] Wed, 12 Feb 2020 08:35:55 UTC (48 KB)
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