MacDonald, Mark (2009) Projective homogeneous varieties birational to quadrics. Documenta Mathematica, 14. pp. 47-66. ISSN 1431-0635
Full text not available from this repository.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: | 12 Nov 2012 10:20 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/59949 |
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