Tilting Bundles and Toric Fano Varieties

  • Nathan Prabhu-Naik

Student thesis: Doctoral ThesisPhD


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 Award3 Nov 2015
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorAlastair Craw (Supervisor)


  • algebraic geometry
  • derived categories
  • Calabi-Yau algebras
  • toric varieties
  • quiver representations

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