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arXiv · 1410.4813

Schottky via the punctual Hilbert scheme

Martin G. Gulbrandsen·Martí Lahoz
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Abstract

We show that a smooth projective curve of genus $g$ can be reconstructed from its polarized Jacobian $(X, Θ)$ 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 $Θ$. 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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Martin G. Gulbrandsen, Martí Lahoz. 2014-10-17. Schottky via the punctual Hilbert scheme. https://arxiv.org/abs/1410.4813

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