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Article

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Accepted version

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2017-12

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/146041

Schottky via the punctual Hilbert scheme

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https://doi.org/10.2748/tmj/1512183632

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.

Subject

Corbes algebraiques, Cicles algebraics

Subject (English)

Algebraic curves, Algebraic cycles

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GULBRANDSEN, Martin G. and LAHOZ VILALTA, Martí. Schottky via the punctual Hilbert scheme. Tohoku Mathematical Journal. 2017. Vol. 69, num. 4, pags. 611-619. ISSN 0040-8735. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/146041

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