Helices on del Pezzo surfaces and tilting Calabi-Yau algebras

Understand

We study tilting for a class of Calabi-Yau algebras associated to helices on Fano varieties.

• We do this by relating the tilting operation to mutations of exceptional collections.
• For helices on del Pezzo surfaces the algebras are of dimension three, and using an argument of Herzog, together with results of Kuleshov and Orlov, we obtain a complete description of the tilting process in terms of quiver mutations.