Characterizing Jacobians via trisecants of the Kummer variety

Pages 485-516 from Volume 172 (2010), Issue 1 by Igor Krichever

Abstract

We prove Welters’ trisecant conjecture: an indecomposable principally polarized abelian variety $X$ is the Jacobian of a curve if and only if there exists a trisecant of its Kummer variety $K(X)$.

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Mathematical Subject Classification
Primary:
DOI
https://doi.org/10.4007/annals.2010.172.485
MR
2680424
zbMATH
1215.14031
Milestones
Received: 19 September 2006
Accepted: 19 November 2007
Published online: 27 June 2010

Authors

Igor Krichever

Department of Mathematics, Columbia University, Rm 527, MC 4434, 2990 Broadway, New York, NY 10027, United States and Landau Institute for Theoretical Physics, Kosygina str. 2, Moscow 119334, >Russia