Projective homogeneous varieties birational to quadrics

Details Projective homogeneous varieties birational to quadrics Projective homogeneous varieties birational to quadrics

2009-03-22

arxiv.org/abs/0903.3698v1

Mathematics

Algebraic Geometry

20 pages, 1 figure

Scientific paper

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).

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