Tilting Bundles and Toric Fano Varieties

Abstract

This thesis constructs tilting bundles obtained from full strong exceptional collections of line bundles on all smooth toric Fano fourfolds. The tilting bundles lead to a large class of explicit Calabi-Yau-5 algebras, obtained as the corresponding rolled-up helix algebra. We provide two different methods to show that a collection of line bundles is full, whilst the strong exceptional condition is checked using the package QuiversToricVarieties for the computer algebra system Macaulay2, written by the author. A database of the full strong exceptional collections can also be found in this package.

Date of Award	3 Nov 2015
Original language	English
Awarding Institution	University of Bath
Supervisor	Alastair Craw (Supervisor)