Tilting generators via ample line bundles

TL;DR

This paper introduces a method to construct tilting generators from ample line bundles on algebraic varieties, providing explicit examples and expanding tools for derived equivalences in algebraic geometry.

Contribution

It presents a novel approach to building tilting generators using ample line bundles, with concrete constructions in multiple examples.

Findings

Constructed tilting generators from ample line bundles in several cases

Established a new method linking ample line bundles to derived equivalences

Enhanced understanding of the relationship between line bundles and non-commutative algebra

Abstract

It is known that a tilting generator on an algebraic variety $X$ gives a derived equivalence between $X$ and a certain non-commutative algebra. In this paper, we explain a method to construct a tilting generator from an ample line bundle, and construct it in several examples.