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 language | English (US) |
|---|---|
| Pages (from-to) | 601-610 |
| Number of pages | 10 |
| Journal | Rocky Mountain Journal of Mathematics |
| Volume | 27 |
| Issue number | 2 |
| State | Published - Mar 1997 |
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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 journal › Article
}
TY - JOUR
T1 - Affine algebraic manifolds without dominant morphisms from Euclidean spaces
AU - Kaliman, Shulim
AU - Makar-Limanov, Leonid
PY - 1997/3
Y1 - 1997/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0031517045&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031517045&partnerID=8YFLogxK
M3 - Article
VL - 27
SP - 601
EP - 610
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 2
ER -