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arXiv · 0903.3698

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 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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Mark L. MacDonald. 2009-03-22. Projective homogeneous varieties birational to quadrics. https://arxiv.org/abs/0903.3698

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