Characterizing Jacobians via trisecants of the Kummer variety

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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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