On the classification of OADP varieties

Details On the classification of OADP varieties On the classification of OADP varieties

2011-05-05

arxiv.org/abs/1105.1007v1

SCIENCE CHINA Mathematics 54 (2011), 1561--1575. Special Issue in honor of Fabrizio Catanese 60^th birthday

Mathematics

Algebraic Geometry

13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in Chin

Scientific paper

10.1007/s11425-010-4164-7

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.

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