Characterizing Jacobians via trisecants of the Kummer Variety

2006/05/23 by I. M. Krichever, I. Krichever, Krichever, I.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.math/0605625

Typos corrected. The version accepted for publication in Advances in Mathematics

openalex publication_date 2006/05/23 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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).

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