Zariski-van Kampen theorems for singular varieties—an approach via the relative monodromy variation
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- Eyral Christophe
- Institute of Mathematics Polish Academy of Sciences
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- Petrov Peter
- Universidade Federal Fluminense Institute of Mathematics and Informatics Bulgarian Academy of Sciences
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説明
<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>
収録刊行物
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- ＫＯＤＡＩ ＭＡＴＨＥＭＡＴＩＣＡＬ ＪＯＵＲＮＡＬ
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ＫＯＤＡＩ ＭＡＴＨＥＭＡＴＩＣＡＬ ＪＯＵＲＮＡＬ 42 (1), 75-98, 2019-03-18
国立大学法人 東京科学大学理学院数学系
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詳細情報 詳細情報について
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- CRID
- 1390282763115688448
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- NII論文ID
- 130007620560
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- ISSN
- 18815472
- 03865991
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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