# name
Schottky via the punctual Hilbert scheme

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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.

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Tohoku Mathematical Journal, 2017, vol. 69, num. 4, p. 611-619

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Schottky via the punctual Hilbert scheme