Geodesic
Minimal canonical dimensions of quadratic forms
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 367-385.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Canonical dimension of a smooth complete connected variety is the minimal dimension of image of its rational endomorphism. The $i$-th canonical dimension of a non-degenerate quadratic form is the canonical dimension of its $i$-th orthogonal grassmannian. The maximum of a canonical dimension for quadratic forms of a fixed dimension is known to be equal to the dimension of the corresponding grassmannian. This article is about the minima of the canonical dimensions of an anisotropic quadratic form. We conjecture that they equal the canonical dimensions of an excellent anisotropic quadratic form of the same dimension and we prove it in a wide range of cases.
Classification : 14L17, 14C25
Keywords: algebraic groups, quadratic forms, projective homogeneous varieties, Chow groups and motives 
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     title = {Minimal canonical dimensions of quadratic forms},
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Karpenko, Nikita A. Minimal canonical dimensions of quadratic forms. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 367-385. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a11/