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Projective manifolds whose topology is strongly reflected in their hyperplane sections

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Abstract

Let ℒ k be the class of complex algebraic k-folds X ⊂ ℙn such that H i(X, ℚ) ≅ H i(H, ℚ) for i≤k−1, H a general hyperplane section. Topological characterizations of - k and several other classes of projective manifolds are given. Moreover, classes ℒ2, ℒ3, ℒ5 are completely described and a partial description of ℒ4 is given. A key role is played by projective bundles.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Via C. Saldini 50, I-20133, Milano, Italy

    Antonio Lanteri

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56100, Pisa, Italy

    Daniele Struppa

Authors
  1. Antonio Lanteri
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  2. Daniele Struppa
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Additional information

Work partially supported by the M.P.I. of the Italian Government.

Both authors are members of the G.N.S.A.G.A. of the Italian C.N.R.

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Lanteri, A., Struppa, D. Projective manifolds whose topology is strongly reflected in their hyperplane sections. Geom Dedicata 21, 357–374 (1986). https://doi.org/10.1007/BF00181538

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  • DOI: https://doi.org/10.1007/BF00181538

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