Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
arXiv:1511.07576 · doi:10.1112/plms.12119
Abstract
We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived category decomposes into zero-dimensional components. For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles.
53 pages, comments welcome!
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- Categorical dimension of birational automorphisms and filtrations of Cremona groups
- Rational points on symmetric powers and categorical representability
- Derived Categories of Quintic Del Pezzo Fibrations
- Involution surface bundles over surfaces
- Deformation of exceptional collections
- Factorization centers in dimension two and the Grothendieck ring of varieties
- Cohomologie non ramifiée de degré 3 : variétés cellulaires et surfaces de del Pezzo de degré au moins 5