On the full, strongly exceptional collections on toric varieties with Picard number three

TL;DR

This paper studies full strongly exceptional collections on smooth complete toric varieties with Picard number three, providing explicit results for many such varieties and exploring their relations with the toric Frobenius morphism.

Contribution

It offers explicit descriptions of strongly exceptional collections for a broad family of Picard number three toric varieties and analyzes their connection to the toric Frobenius morphism.

Findings

Explicit collections for many Picard number three varieties

Relations between collections and Frobenius pushforward

Extension of known results to new families

Abstract

We investigate full strongly exceptional collections on smooth, com- plete toric varieties. We obtain explicit results for a large family of varieties with Picard number three, containing many of the families already known. We also describe the relations between the collections and the split of the push forward of the trivial line bundle by the toric Frobenius morphism.