Polynomials with general C^2-fibers are variables. I
代数几何
2007-05-23 v1
摘要
Suppose that X' is a smooth affine algebraic variety of dimension 3 with H_3(X')=0 which is a UFD and whose invertible functions are constants. Suppose that Z is 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 C^2. We prove that X' is isomorphic to C^3 iff none of irreducible components of X'-Z has non-isolated singularities. Furthermore, if X' is C^3 then p extends to a polynomial on C^3 which is linear in a suitable coordinate system. As a consequence we obtain the fact formulated in the title of the paper.
引用
@article{arxiv.math/9912058,
title = {Polynomials with general C^2-fibers are variables. I},
author = {Shulim Kaliman},
journal= {arXiv preprint arXiv:math/9912058},
year = {2007}
}