Characterizing Jacobians of algebraic curves with involution

2021/09/27 by I. M. Krichever, Krichever, Igor
Computer Science · Mathematics · #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) #Mathematical Physics (math-ph) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2109.13161

openalex publication_date 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give two characterizations of Jacobians of curves with involution having fixed points in the framework of two particular cases of Welter's trisecant conjecture. The geometric form of each of these characterizations is the statement that such Jacobians are exactly those containing a shifted Abelian subvariety whose image under the Kummer map is orthogonal to an explicitly given vector.

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