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Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras

Lutz Hille;  Markus Perling — 2014

Annales de l’institut Fourier

Let X be any rational surface. We construct a tilting bundle T on X . Moreover, we can choose T in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of finitely generated modules over a finite dimensional quasi-hereditary algebra A . The construction starts with a full exceptional sequence of line bundles on X and uses universal extensions. If X is any smooth projective variety...

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