Rational surfaces and canonical dimension of PGL_6

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dc.creatorColliot-Thélène, Jean-Louis
dc.creatorKarpenko, Nikita A.
dc.creatorMerkurjev, Alexander S.
dc.date2006-11-25
dc.date.accessioned2026-07-07T07:33:19Z
dc.date.available2026-07-07T07:33:19Z
dc.descriptionThe "canonical dimension" of an algebraic group over a field by definition is the maximum of the canonical dimensions of principal homogenous spaces under that group. Over a field of characteristic zero, we prove that the canonical dimension of the projective linear group PGL_6 is 3. We give two distinct proofs, both of which rely on the birational classification of rational surfaces over a nonclosed field. One of the proofs involves taking a novel look at del Pezzo surfaces of degree 6.
dc.identifierhttps://arxiv.org/abs/math/0611777
dc.identifierhttp://arxiv.org/abs/math/0611777
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119416
dc.subjectAlgebraic Geometry
dc.subject20G15; 14J26
dc.titleRational surfaces and canonical dimension of PGL_6
dc.typetext

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