Projective homogeneous varieties birational to quadrics

  • Mark L. MacDonald

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Abstract

We will consider an explicit birational map between a quadric and the projective variety of traceless rank one elements in a simple reduced Jordan algebra is a homogeneous -variety for the automorphism group . 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 .

Cite this article

Mark L. MacDonald, Projective homogeneous varieties birational to quadrics. Doc. Math. 14 (2009), pp. 47–66

DOI 10.4171/DM/265