Projective homogeneous varieties birational to quadrics

MacDonald, Mark (2009) Projective homogeneous varieties birational to quadrics. Documenta Mathematica, 14. pp. 47-66. ISSN 1431-0635

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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 $G=\textup{Aut}(J)$. 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 $X(J)$.

Item Type:
Journal Article
Journal or Publication Title:
Documenta Mathematica
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
59949
Deposited By:
Deposited On:
12 Nov 2012 10:20
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 08:13