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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...

Divisorial cohomology vanishing on toric varieties.

Perling, Markus — 2011

Documenta Mathematica

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