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Mathematische Annalen

, Volume 344, Issue 3, pp 597–617 | Cite as

Varieties with quadratic entry locus, I

  • Francesco RussoEmail author
Article

Abstract

We introduce and study (L)QEL-manifolds \({X \subset \mathbb P^N}\) of type δ, a class of projective varieties whose extrinsic and intrinsic geometry is very rich, especially when δ >  0. We prove a strong Divisibility Property for LQEL-manifolds of type δ ≥  3, allowing the classification of those of type \({\delta \geq \frac{dim(X)}{2}}\) . In particular we obtain a new and very short proof that Severi varieties have dimension 2,4, 8 or 16 and also an almost self-contained proof of their classification due to Zak. We also provide the classification of special Cremona transformations of type (2,3) and (2,5).

Keywords

Irreducible Component Projective Variety Fano Manifold Secant Variety Segre Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di CataniaCataniaItaly

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