2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157353We 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 MathematicsAlgebraic GeometryHigh Energy Physics - Theorytext