Varieties with quadratic entry locus, I

By Francesco Russo. 2007

56 citations recorded by the source corpus.

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).

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/618242785e338f8eb90f9d0183cf5dd27df3e2d9