Varieties with quadratic entry locus, II

Abstract

We continue the study, begun by the second author in math.AG/0701889, of secant defective manifolds having "simple entry loci". We prove that such manifolds are rational and describe them in terms of tangential projections. Using also our results in math.AG/0701885, their classification is reduced to the case of Fano manifolds of high index, whose Picard group is generated by the hyperplane section class. Conjecturally, the former should be linear sections of rational homogeneous manifolds. We also provide evidence that the classification of linearly normal dual defective manifolds with Picard group generated by the hyperplane section should follow along the same lines.

15 pages. Minor changes. Final version. To appear in Compositio Mathematica

Cited by in corpus (8)

• Varieties with quadratic entry locus, I
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• Lines on projective varieties and applications
• On the classification of OADP varieties
• Quadro-quadric special birational transformations of projective spaces
• Projective and birational geometry of Grassmannians and other special varieties
• Varieties Connected by Chains of Lines
• Remarks on defective Fano manifolds