Frobenius splitting and Derived category of toric varieties

TL;DR

This paper explores Frobenius splitting on Fano toric varieties to explicitly construct an orthogonal basis of line bundles in their derived categories, enhancing understanding of their geometric and categorical structure.

Contribution

It introduces a method to explicitly construct an orthogonal basis of line bundles in the derived category of Fano toric varieties using Frobenius splitting.

Findings

Explicit orthogonal basis of line bundles constructed

Application to Fano toric varieties with high Picard number

Enhanced understanding of derived categories of toric varieties

Abstract

The splitting of the Frobenius direct image of line bundles on toric varieties is used to explicitly construct an orthogonal basis of line bundles in the derived category D^b(X) where X is a Fano toric variety with (almost) maximal Picard number.