Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection

TL;DR

This paper establishes a bijection between strata of oriented toric hyperplane arrangements and lattice points in zonotopes, linking geometric combinatorics with algebraic geometry and derived categories.

Contribution

It introduces a novel correspondence connecting hyperplane arrangement strata with zonotope lattice points and relates this to toric varieties and their derived categories.

Findings

Strata of hyperplane arrangements correspond to zonotope lattice points

Dimension of strata relates to minimal face dimension of zonotope

Connection to Bondal-Thomsen generators in derived categories

Abstract

We show that strata of oriented toric hyperplane arrangements are in bijection with a collection of lattice points in a zonotope. Moreover, we relate the dimension of the stratum and the dimension of the minimal face of the zonotope containing the corresponding lattice point. We discuss how this correspondence is related to toric varieties and the Bondal-Thomsen generators of their derived categories.