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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: Article
Journal or Publication Title: Documenta Mathematica
Uncontrolled Keywords: Motivic decompositions ; Sarkisov links ; Jordan algebras
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 59949
Deposited By: ep_importer_pure
Deposited On: 12 Nov 2012 10:20
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 12:45
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59949

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