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The Lefschetz Theorem for Hyperplane Sections

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Handbook of Geometry and Topology of Singularities I

Abstract

In these notes we consider different theorems of the Lefschetz type. We start with the classical Lefschetz Theorem for hyperplane sections on a non-singular projective variety. We show that this extends to the cases of a non-singular quasi-projective variety and to singular varieties. We also consider local forms of theorems of the Lefschetz type.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Münster, Münster, Germany

    Helmut A. Hamm

  2. Centre de Mathématiques et Informatique, Université d’Aix-Marseille, Marseille, France

    Dũng Tráng Lê

Authors
  1. Helmut A. Hamm
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  2. Dũng Tráng Lê
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Correspondence to Helmut A. Hamm .

Editor information

Editors and Affiliations

  1. Unidad Cuernavaca Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, Mexico

    José Luis Cisneros Molina

  2. Centre de Mathématiques et Informatique, Université d’Aix-Marseille, Marseille, France

    Dũng Tráng Lê

  3. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    José Seade

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Hamm, H.A., Lê, D.T. (2020). The Lefschetz Theorem for Hyperplane Sections. In: Cisneros Molina, J.L., Lê, D.T., Seade, J. (eds) Handbook of Geometry and Topology of Singularities I. Springer, Cham. https://doi.org/10.1007/978-3-030-53061-7_9

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