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 language | English (US) |
|---|---|
| Pages (from-to) | 161-190 |
| Number of pages | 30 |
| Journal | Pacific Journal of Mathematics |
| Volume | 203 |
| Issue number | 1 |
| State | Published - 2002 |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Polynomials with general C2-fibers are variables
AU - Kaliman, Shulim
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0036347427&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036347427&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0036347427
VL - 203
SP - 161
EP - 190
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 1
ER -