Derived categories of toric Fano 3-folds via the Frobenius morphism

Abstract

In [8, Conjecture 3.6], Costa and Miró-Roig state the following conjecture:Every smooth complete toric Fano variety has a full strongly exceptional collection of line bundles. The goal of this article is to prove it for toric Fano 3-folds.

Keywords

• Derived Categories
• Toric Fano 3-Folds
• Frobenius Splitting
• Full Strongly Excep- tional Sequences
• King’s conjecture