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 Hilb(J) containing the Abel-Jacobi embedding as a point. We relate the result to the ramification (and to the fibres) of the Torelli morphism M-g -> 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.
The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves / Ricolfi, A. T.. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - 14:6(2020), pp. 1381-1397. [10.2140/ant.2020.14.1381]
The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves
Ricolfi, A. T.
Writing – Original Draft Preparation
2020-01-01
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 Hilb(J) containing the Abel-Jacobi embedding as a point. We relate the result to the ramification (and to the fibres) of the Torelli morphism M-g -> 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.| File | Dimensione | Formato | |
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