Rational surfaces and the canonical dimension of $\operatorname {\mathbf {PGL}}_6$

DOI10.1090/S1061-0022-08-01021-2zbMath1206.14070arXivmath/0611777OpenAlexW2023055433MaRDI QIDQ3079222

Jean-Louis Colliot-Thélène, Nikita A. Karpenko, Alexander S. Merkurjev

Publication date: 2 March 2011

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611777

zbMATH Keywords

birational classificationcanonical dimensionrational surfacesalgebraic groupprojective linear group

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Linear algebraic groups over arbitrary fields (20G15) Group actions on varieties or schemes (quotients) (14L30) Group schemes (14L15)

Related Items

Finite quasisimple groups acting on rationally connected threefolds ⋮ Essential dimension and genericity for quiver representations ⋮ Birational classification of pointless del Pezzo surfaces of degree 8 ⋮ On the essential dimension of cyclic groups ⋮ Morphisms to Brauer–Severi Varieties, with Applications to Del Pezzo Surfaces ⋮ Essential dimension of moduli of curves and other algebraic stacks ⋮ Del Pezzo surfaces of degree 6 over an arbitrary field ⋮ Toric surfaces over an arbitrary field ⋮ Odd order obstructions to the Hasse principle on general K3 surfaces ⋮ Del Pezzo surfaces over finite fields and their Frobenius traces ⋮ Models of triple covers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Desingularization of two-dimensional schemes
• Every rational surface is separably split
• Canonical \(p\)-dimension of algebraic groups
• On the notion of canonical dimension for algebraic groups
• The Index of a Brauer Class on a Brauer-Severi Variety
• The multipliers of similitudes and the Brauer group of homogeneous varieties.
• Steenrod operations and degree formulas
• Canonicalp-dimensions of algebraic groups and degrees of basic polynomial invariants
• Threefolds whose canonical bundles are not numerically effective