We continue the study, begun in [F. Russo, Varieties with quadratic entry locus. I, Preprint (2006), 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 the work of [P.Ionescu and F.Russo, Conic-connected manifolds, Preprint (2006), 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 homogeneousmanifolds. 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. © 2008 Copyright Foundation Compositio Mathematica 2008.
Varieties with quadratic entry locus. II
IONESCU, Paltin;
2008
Abstract
We continue the study, begun in [F. Russo, Varieties with quadratic entry locus. I, Preprint (2006), 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 the work of [P.Ionescu and F.Russo, Conic-connected manifolds, Preprint (2006), 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 homogeneousmanifolds. 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. © 2008 Copyright Foundation Compositio Mathematica 2008.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
