BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Tilting bundles, BGG-correspondence, higher preprojective algebras and the Serre functor Hille, Lutz


We report on a work jointly started with Ragnar Buchweitz about the pull back of a tilting bundle T to the total space of the canonical line bundle Y. Let X be an algebraic variety with a tilting bundle T, then we have a criterion when its pull back to Y is also a tilting bundle. This is closely related to my previous work on distinguished tilting sequences and generalizes the results therein. Morover, we can compute the endomorphism ring of the pull back tilting bundle as the higher preprojective algebra. This leads to a geometric construction of those algebras. The construction needs tilting bundles T with endomorphism algebra of global dimension dimX. In this talk we consider several examples for surfaces and compute the possible global dimensions of A.

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