Equivariant vector bundles on toric schemes over semirings

2024/06/11 by Jun, Jaiung, Mincheva, Kalina, Tolliver, Jeffrey
#14A23 #14C22 #14T10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.06933

Abstract

We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme X over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group Pic_G(X). Finally, we prove a version of Klyachko's classification theorem for toric vector bundles over an idempotent semifield.

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