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Article Dans Une Revue Indagationes Mathematicae Année : 2003

Scorza varieties and Jordan algebras

Pierre-Emmanuel Chaput

Résumé

The Severi and Scorza varieties are the limiting cases of a theorem of Zak conjectured by Hartshorne. Zak also classified the Severi and Scorza varieties. Surprisingly enough, there are only 4 Severi varieties, one for each dimension 2,4,8 and 16 and they are homogeneous and very strongly linked with the 4 rank-3 Jordan algebras. In this article, I give several variations of Zak's classification theorem, proving a priori the homogeneity of Scorza varieties, and showing how it is possible to give a Jordan structure to the ambient space of a Scorza variety.

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Dates et versions

hal-01256848 , version 1 (15-01-2016)

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Pierre-Emmanuel Chaput. Scorza varieties and Jordan algebras. Indagationes Mathematicae, 2003, 14 (2), pp.169-182. ⟨hal-01256848⟩
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