A note on dual abelian varieties

2023/11/05 by Aleksandra Borówka, Borówka, Aleksandra, Paweł Borówka +1 · 1 citation
Mathematics · Physics and Astronomy · #14K02 #14K12 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2311.02718

openalex publication_date 2023/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any non-principal polarisation D, we explicitly construct D-polarised abelian variety A, such that its dual abelian variety is not (abstractly) isomorphic to A. For dim(A)>3 the construction includes examples with submaximal Picard number equal to (dim(A)-1)²+1. As a corollary, we show that a very general non-principally polarised abelian variety is not isomorphic to its dual. Moreover, we show an example of an abelian variety that is isomorphic to its dual, yet it does not admit a principal polarisation.

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