Displaying similar documents to “Sums of squares and quadratric forms in real algebraic geometry”

Birational geometry of quadrics

Burt Totaro (2009)

Bulletin de la Société Mathématique de France

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We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension...

Quadratic forms over fields

K. Szymiczek

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CONTENTSIntroduction.................................................................................................................................. 5Chapter I. Preliminaries oil round and Pfister forms.......................................................... 8Chapter II. Basic properties of the Grothendieck ring......................................................... 11 § 1. Prime ideals in G(F).........................................................................................................