Uniform Zariski's theorem on fundamental groups

Research output: Contribution to journalArticle

Abstract

The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of the fundamental groups of the complements to the hypersurface in the plane and in the space. If a family of hypersurfaces depends algebraically on parameters then it is not true in general that there exists a plane such that the natural embedding generates an isomorphism of the fundamental groups of the complements to each hypersurface from this family in the plane and in the space. But we show that in the affine case such a plane exists after a polynomial coordinate substitution.

Original languageEnglish (US)
Pages (from-to)323-343
Number of pages21
JournalIsrael Journal of Mathematics
Volume116
StatePublished - 2000

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Fundamental Group
Hypersurface
Theorem
Affine Space
Projective Space
Isomorphism
Complement
Substitution
Polynomial
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Uniform Zariski's theorem on fundamental groups. / Kaliman, Shulim.

In: Israel Journal of Mathematics, Vol. 116, 2000, p. 323-343.

Research output: Contribution to journalArticle

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