Compositio Mathematica

The Chow ring of the Cayley plane

Atanas Iliev a1 and Laurent Manivel a2
a1 Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria
a2 Institut Fourier, Laboratoire de Mathématiques, UMR 5582 (UJF-CNRS), BP 74, 38402 St Martin d'Hères, France

Article author query
iliev a   [Google Scholar] 
manivel l   [Google Scholar] 


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.

(Received July 14 2003)
(Accepted October 15 2003)
(Published Online December 1 2004)

Key Words: Chow ring; Cayley plane; Severi variety.

Maths Classification

14M17; 14N15.