Zariski-van Kampen theorems for singular varieties—an approach via the relative monodromy variation

DOI
  • Eyral Christophe
    Institute of Mathematics Polish Academy of Sciences
  • Petrov Peter
    Universidade Federal Fluminense Institute of Mathematics and Informatics Bulgarian Academy of Sciences

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Description

<p>The classical Zariski-van Kampen theorem gives a presentation of the fundamental group of the complement of a complex algebraic curve in P2. The first generalization of this theorem to singular (quasi-projective) varieties was given by the first author. In both cases, the relations are generated by the standard monodromy variation operators associated with the special members of a generic pencil of hyperplane sections. In the present paper, we give a new generalization in which the relations are generated by the relative monodromy variation operators introduced by D. Chéniot and the first author. The advantage of using the relative operators is not only to cover a larger class of varieties but also to unify the Zariski-van Kampen type theorems for the fundamental group and for higher homotopy groups. In the special case of non-singular varieties, the main result of this paper was conjectured by D. Chéniot and the first author.</p>

Journal

  • Kodai Mathematical Journal

    Kodai Mathematical Journal 42 (1), 75-98, 2019-03-18

    Institute of Science Tokyo, Department of Mathematics

Keywords

Details 詳細情報について

  • CRID
    1390282763115688448
  • NII Article ID
    130007620560
  • DOI
    10.2996/kmj/1552982507
  • ISSN
    18815472
    03865991
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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