Tropicalization of linear series and tilings by polymatroids

TL;DR

This paper explores how tropicalization of linear series on curves leads to complex tilings by polymatroids, connecting tropical geometry, non-Archimedean analysis, and algebraic geometry through a new general framework.

Contribution

It introduces a novel framework for tilings of vector spaces by polymatroids derived from tropical and non-Archimedean geometry, linking to Chow quotients of Grassmannians.

Findings

Tropicalization induces two-parameter families of polymatroid tilings.

The tilings are shown to be regular and structurally related to Chow quotients.

Framework unifies tropical geometry, non-Archimedean analysis, and algebraic geometry.

Abstract

We show that tropicalization of linear series on curves gives rise to two-parameter families of tilings by polymatroids, with one parameter arising from the theory of divisors on tropical curves and the other from the reduction of linear series of rational functions in non-Archimedean geometry. In order to do this, we introduce a general framework that produces tilings of vector spaces and their subsets by polymatroids. We furthermore show that these tilings are regular and relate them to work by Kapranov and Lafforgue on Chow quotients of Grassmannians.