Gulbrandsen, Martin G.Lahoz Vilalta, Martí2019-12-042019-12-042017-120040-8735https://hdl.handle.net/2445/146041We 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.9 p.application/pdfeng(c) Tohoku Mathematical Journal, 2017Corbes algebraiquesCicles algebraicsAlgebraic curvesAlgebraic cyclesinfo:eu-repo/semantics/article6929982019-12-04info:eu-repo/semantics/openAccess