Geodesic
Projective homogeneous varieties birational to quadrics
Documenta mathematica, Tome 14 (2009), pp. 47-66
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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).
DOI : 10.4171/dm/265
Classification : 11E04, 14C15, 14E05, 14L30
Mots-clés : motivic decompositions, sarkisov links, Jordan algebras 
@article{10_4171_dm_265,
     author = {Mark L. MacDonald},
     title = {Projective homogeneous varieties birational to quadrics},
     journal = {Documenta mathematica},
     pages = {47--66},
     year = {2009},
     volume = {14},
     doi = {10.4171/dm/265},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/265/}
}
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Mark L. MacDonald. Projective homogeneous varieties birational to quadrics. Documenta mathematica, Tome 14 (2009), pp. 47-66. doi: 10.4171/dm/265

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