Vector bundles on tropical schemes

2020/09/07 by Jun, Jaiung, Mincheva, Kalina, Tolliver, Jeffrey · 1 citation
#14C22 #14T10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2009.03030

Abstract

We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, which provide the necessary algebraic background for the theory (2) we relate vector bundles on tropical schemes to topological vector bundles and vector bundles on monoid schemes, and finally (3) we show that all line bundles on a tropical scheme can be lifted to line bundles on a usual scheme in the affine case.

Cited by

• On Ehrhart theory for tropical vector bundles

Related

• Tropical Vector Bundles
• Tropical schemes, tropical cycles, and valuated matroids
• Chern classes of tropical vector bundles
• Geometry over the tropical dual numbers
• Tropical vector bundles and matroids