Let S_k be the class of complex algebraic k-folds X \subset P^n such that H_i(X,Q) \cong H_i(H,Q) for i \leq k-1, H being a general hyperplane section. Topological characterizations of S_k and several other classes of projective manifolds are given. Moreover, classes S_2, S_3, S_5 are completely described and a partial description of S_4 is given. A key role is played by projective bundles.

Projective manifolds whose topology is strongly reflected in their hyperplane sections / A. Lanteri, D. Struppa. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 21:3(1986), pp. 357-374.

### Projective manifolds whose topology is strongly reflected in their hyperplane sections

#### Abstract

Let S_k be the class of complex algebraic k-folds X \subset P^n such that H_i(X,Q) \cong H_i(H,Q) for i \leq k-1, H being a general hyperplane section. Topological characterizations of S_k and several other classes of projective manifolds are given. Moreover, classes S_2, S_3, S_5 are completely described and a partial description of S_4 is given. A key role is played by projective bundles.
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projective manifold; hyperplane section; Lefschetz theorem; scrolls; defective manifold
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/189304
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