Mark.L.MacDonald@googlemail.com

Submission: 2009, Mar 21

We will consider an explicit birational map between a quadric and the projective variety X(J) of traceless rank one elements in a simple reduced Jordan algebra J. X(J) is a homogeneous G-variety for the automorphism group G=Aut(J). We will show that the birational map is a blow up followed by a blow down. This will allow us to use the blow up formula for motives together with Vishik's work on the motives of quadrics to give a motivic decomposition of X(J).

2000 Mathematics Subject Classification: Primary 11E04; Secondary 14E05, 14L30, 14C15

Keywords and Phrases: Motivic decompositions, Sarkisov links, Jordan algebras

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