Tilting Bundles on Toric Fano Fourfolds

TL;DR

This paper constructs tilting bundles on all smooth 4-dimensional toric Fano varieties, leading to explicit Calabi-Yau-5 algebras and providing a computational database for these structures.

Contribution

It introduces a method to build tilting bundles from exceptional collections on all smooth 4D toric Fano varieties, expanding the toolkit for algebraic and geometric analysis.

Findings

Constructed tilting bundles for all smooth 4D toric Fano varieties.

Generated a large class of explicit Calabi-Yau-5 algebras.

Provided a computational database via Macaulay2 package.

Abstract

This paper constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth $4$-dimensional toric Fano varieties. The tilting bundles lead to a large class of explicit Calabi-Yau-$5$ algebras, obtained as the corresponding rolled-up helix algebra. A database of the full strong exceptional collections can be found in the package QuiversToricVarieties for the computer algebra system Macaulay2.