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

DOI10.1112/plms.12119zbMath1435.14015arXiv1511.07576OpenAlexW2178202678WikidataQ130209701 ScholiaQ130209701MaRDI QIDQ4583326

Marcello Bernardara, Asher Auel

Publication date: 28 August 2018

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07576

zbMATH Keywords

derived categoriesrational pointsdel Pezzo surfacessemiorthogonal decomposition

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Brauer groups (algebraic aspects) (16K50) Quadratic spaces; Clifford algebras (11E88) Rationality questions in algebraic geometry (14E08) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

Related Items (16)

Categorical dimension of birational transformations and filtrations of Cremona groups ⋮ Derived Categories of Families of Sextic del Pezzo Surfaces ⋮ Rational maps between varieties associated to central simple algebras ⋮ Derived categories of centrally‐symmetric smooth toric Fano varieties ⋮ On nonexistence of full exceptional collections on some relative flags ⋮ Forms of del Pezzo surfaces of degree $5$ and $6$ ⋮ Semiorthogonal decompositions in families ⋮ Involution surface bundles over surfaces ⋮ Fibrations in sextic del Pezzo surfaces with mild singularities ⋮ Derived categories of quintic del Pezzo fibrations ⋮ Descent for semiorthogonal decompositions ⋮ No phantoms in the derived category of curves over arbitrary fields, and derived characterizations of Brauer-Severi varieties ⋮ Cycles, derived categories, and rationality ⋮ Rational points and derived equivalence ⋮ On derived categories of arithmetic toric varieties ⋮ Models of quadric surface bundles

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