arXiv subjects

Davis Painter

Publications and source records attributed to Davis Painter.

2 recordsLinked to original sources

arXiv2025

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

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.

math.CO↗

arXiv2024

Rational points of fixed denominator in real toric arrangements

We give a sufficient condition on a positive integer $m$ for every stratum of a given real toric hyperplane arrangement to contain a rational point of denominator $m$. As a consequence, we give a sufficient condition on $m$ for the degree $m$ Frobenius pushforward of the structure sheaf on a smooth toric variety to contain all possible summands in the Picard group.

math.CO↗