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 $\dim X$. In this talk we consider several examples for surfaces and compute the possible global dimensions of $A$.

This work was supportes by CRC 878, 'Groups Geometry and Actions' and by Mathematics Münster: 'Dynamics–Geometry–Structure'.