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1 results

  • Varieties with quadratic entry locus, II

  • Part of
  • Paltin Ionescu, Francesco Russo
  • Journal:
    Compositio Mathematica / Volume 144 / Issue 4 / July 2008
    Published online by Cambridge University Press:
    01 July 2008, pp. 949-962
    Print publication:
    July 2008
    • Article
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  • 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 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.