Affine algebraic manifolds without dominant morphisms from Euclidean spaces

Shulim Kaliman, Leonid Makar-Limanov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We develop a method which in some cases enables us to establish the absence of dominant morphisms from Euclidean spaces into affine algebraic manifolds which are hypersurfaces in Cn. This approach shows that many of recently constructed smooth contractible hypersurfaces in Cn, n ≥ 4, are not isomorphic to Euclidean spaces and cannot be used as counterexamples to the Zariski cancellation conjecture, to the Abhyankar-Sathaye conjecture, and to the problem of linearizing a C*-action on C3.

Original languageEnglish (US)
Pages (from-to)601-610
Number of pages10
JournalRocky Mountain Journal of Mathematics
Volume27
Issue number2
StatePublished - Mar 1997

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Morphisms
Hypersurface
Euclidean space
Cancellation
Counterexample
Isomorphic

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Affine algebraic manifolds without dominant morphisms from Euclidean spaces. / Kaliman, Shulim; Makar-Limanov, Leonid.

In: Rocky Mountain Journal of Mathematics, Vol. 27, No. 2, 03.1997, p. 601-610.

Research output: Contribution to journalArticle

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