Severi，Scorza簇与Jordan代数
Severi, Scorza varieties and Jordan algebras
摘要：
Severi和Scorza簇是Hartshorne证明的Zak定理的极限情形。Zak还对Severi和Scorza品种进行了分类。令人惊讶的是，只有4个Severi变种，每个维度为2，4，8和16，它们是齐次的，并且与4个秩3 Jordan代数有很强的联系。在这篇文章中，我给几个变化扎克的分类定理，先验证明的同质性的Scorza品种，并显示它是如何可能给一个约旦结构的周围空间的Scorza品种。
英文摘要：
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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