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The Chow ring of the Cayley plane

Published online by Cambridge University Press:  01 December 2004

Atanas Iliev  and
Laurent Manivel
Atanas Iliev
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, [email protected]
Laurent Manivel
Affiliation:
Institut Fourier, Laboratoire de Mathématiques, UMR 5582 (UJF-CNRS), BP 74, 38402 St Martin d'Hères, [email protected]
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Abstract

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We give a full description of the Chow ring of the complex Cayley plane $\mathbb{O}\mathbb{P}^2$. For this, we describe explicitly the most interesting of its Schubert varieties and compute their intersection products. Translating our results into the Borel presentation, i.e. in terms of Weyl group invariants, we are able to compute the degree of the variety of reductions Y8 introduced by the current authors in arXiv: math.AG/0306328.

Keywords

Chow ringCayley planeSeveri variety14M1714N15
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 1 , January 2005 , pp. 146 - 160
Copyright
Foundation Compositio Mathematica 2005