Characterizing Jacobians via trisecants of the Kummer variety


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 $K(X)$.


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