Polynomials with general C2-fibers are variables

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Abstract

Let X′ be a complex affine algebraic threefold with H3(X′) = 0 which is a UFD and whose invertible functions are constants. Let Z be a Zariski open subset of X′ which has a morphism p : Z → U into a curve U such that all fibers of p are isomorphic to C2. We prove that X′ is isomorphic to C3 iff none of irreducible components of X′ \ Z has non-isolated singularities. Furthermore, if X′ is C3 then p extends to a polynomial on C3 which is linear in a suitable coordinate system. This implies the fact formulated in the title of the paper.

Original languageEnglish (US)
Pages (from-to)161-190
Number of pages30
JournalPacific Journal of Mathematics
Volume203
Issue number1
StatePublished - 2002

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Isomorphic
Fiber
Nonsingularity
Polynomial
Irreducible Components
Threefolds
Morphism
Invertible
Imply
Curve
Subset

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Polynomials with general C2-fibers are variables. / Kaliman, Shulim.

In: Pacific Journal of Mathematics, Vol. 203, No. 1, 2002, p. 161-190.

Research output: Contribution to journalArticle

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