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arXiv · 1804.08481

The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves

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.

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Andrea T. Ricolfi. 2020-02-12. The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves. https://doi.org/10.2140/ant.2020.14.1381

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