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