%0 Journal Article
%T Schottky via the punctual Hilbert scheme
%A Martin G. Gulbrandsen
%A Mart¨ª Lahoz
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1410.4813v1