Characterizing Jacobians via trisecants of the Kummer Variety

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We prove Welter's 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 $K(X)$.
Typos corrected. The version accepted for publication in Advances in Mathematics

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