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Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields

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 نشر من قبل Asher Auel
 تاريخ النشر 2015
  مجال البحث
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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.



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