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Title: Schottky via the punctual Hilbert scheme
Author: Gulbrandsen, Martin G.
Lahoz Vilalta, Martí
Keywords: Corbes algebraiques
Cicles algebraics
Algebraic curves
Algebraic cycles
Issue Date: Dec-2017
Publisher: Tohoku University
Abstract: We show that a smooth projective curve of genus $g$ can be reconstructed from its polarized Jacobian $(X, \Theta)$ as a certain locus in the Hilbert scheme $\mathrm{Hilb}^{d}(X)$ for $d=3$ and for $d=g+2$ defined by geometric conditions in terms of the polarization $\Theta$. The result is an application of the Gunning-Welters trisecant criterion and the Castelnuovo-Schottky theorem by Pareschi-Popa and Grushevsky, and its scheme theoretic extension by the authors.
It is part of: Tohoku Mathematical Journal, 2017, vol. 69, num. 4, p. 611-619
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ISSN: 0040-8735
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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