The toric Frobenius morphism and a conjecture of Orlov

TL;DR

This paper explores the use of the toric Frobenius morphism and exceptional collections to verify Orlov's Conjecture on derived dimension for certain toric varieties.

Contribution

It combines the Bondal-Uehara method with recent results to extend the class of toric varieties satisfying Orlov's Conjecture.

Findings

Expanded the set of toric varieties satisfying Orlov's Conjecture

Connected the toric Frobenius morphism with derived dimension

Demonstrated the effectiveness of exceptional collections in this context

Abstract

We combine the Bondal-Uehara method for producing exceptional collections on toric varieties with a result of the first author and Favero to expand the set of varieties satisfying Orlov's Conjecture on derived dimension.