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Projective homogeneous varieties birational to quadrics

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Projective homogeneous varieties birational to quadrics. / MacDonald, Mark.
In: Documenta Mathematica, Vol. 14, 2009, p. 47-66.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

MacDonald, M 2009, 'Projective homogeneous varieties birational to quadrics', Documenta Mathematica, vol. 14, pp. 47-66. <http://www.math.uiuc.edu/documenta/vol-14/03.html>

APA

MacDonald, M. (2009). Projective homogeneous varieties birational to quadrics. Documenta Mathematica, 14, 47-66. http://www.math.uiuc.edu/documenta/vol-14/03.html

Vancouver

MacDonald M. Projective homogeneous varieties birational to quadrics. Documenta Mathematica. 2009;14:47-66.

Author

MacDonald, Mark. / Projective homogeneous varieties birational to quadrics. In: Documenta Mathematica. 2009 ; Vol. 14. pp. 47-66.

Bibtex

@article{a2a702138d2045df94e8cde09fa659c8,
title = "Projective homogeneous varieties birational to quadrics",
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 $X(J)$.",
keywords = "Motivic decompositions, Sarkisov links , Jordan algebras",
author = "Mark MacDonald",
year = "2009",
language = "English",
volume = "14",
pages = "47--66",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",

}

RIS

TY - JOUR

T1 - Projective homogeneous varieties birational to quadrics

AU - MacDonald, Mark

PY - 2009

Y1 - 2009

N2 - 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 $X(J)$.

AB - 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 $X(J)$.

KW - Motivic decompositions

KW - Sarkisov links

KW - Jordan algebras

M3 - Journal article

VL - 14

SP - 47

EP - 66

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

ER -