Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization

2023/12/20 by Gross, Andreas, Kaur, Inder, Ulirsch, Martin +1 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.12980

Abstract

We construct a moduli space of semi-homogeneous vector bundles with a fixed Néron-Severi class H on an abelian variety A over an algebraically closed field of characteristic zero. When A has totally degenerate reduction over a non-Archimedean field, we describe our moduli space from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For H=0 our moduli space may be identified with the moduli space M_0,r(A) of semistable vector bundles with vanishing Chern classes on A. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of A onto M_0,r(A), which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of M_0,r(A).

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