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Parameter spaces for quadrics

Anders Thorup (1996)

Banach Center Publications

The parameter spaces for quadrics are reviewed. In addition, an explicit formula for the number of quadrics tangent to given linear subspaces is presented.

Pfaffians, central simple algebras and similtudes.

R. Sridharan, M.-A. Knus, R. Parimala (1991)

Mathematische Zeitschrift

Pfister Ideals in Witt Rings.

T.Y. Lam, R. Elman, A.R. Wadsworth (1979)

Mathematische Annalen

Pfister's conjecture on quadratic Co-fields.

David B. Leep (1990)

Journal für die reine und angewandte Mathematik

Primitive representation of a binary quadratic form as a sum of four squares

John Hunsucker (1971)

Acta Arithmetica

Principe de Hasse pour les espaces principaux homogènes sous les groupes classiques sur un corps de dimension cohomologique virtuelle au plus 1.

Antoine Ducros (1996)

Manuscripta mathematica

Projective geometry for orthogonal groups.

D.G. James (1980)

Journal für die reine und angewandte Mathematik

Projective homogeneous varieties birational to quadrics.

MacDonald, Mark L. (2009)

Documenta Mathematica

Proper cycles of indefinite quadratic forms and their right neighbors

Ahmet Tekcan (2007)

Applications of Mathematics

In this paper we consider proper cycles of indefinite integral quadratic forms $F = (a, b, c)$ with discriminant $Δ$ . We prove that the proper cycles of $F$ can be obtained using their consecutive right neighbors $R^{i} (F)$ for $i \geq 0$ . We also derive explicit relations in the cycle and proper cycle of $F$ when the length $l$ of the cycle of $F$ is odd, using the transformations $τ (F) = (- a, b, - c)$ and $χ (F) = (- c, b, - a)$ .

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