Polynomials with general C2–fibers are variables
Polynomials with general C2–fibers are variables
复制标题
具有一般 C2 纤维的多项式是变量
DOI：
10.2140/pjm.2002.203.161
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发表时间：
2002
影响因子：
0.6
通讯作者：
S. Kaliman
中科院分区：
文献类型：
--
作者：
S. Kaliman
设X'为复仿射代数三重，H 3 (X') = 0，其为UFD且其可逆函数为常数。令 Z 为 X' 的 Zariski 开子集，其具有态射 p : Z → U 到曲线 U 中，使得 p 的所有纤维与 C 2 同构。我们证明 X' 与 C 3 同构，当且仅当 X'\ Z 的不可约分量都不具有非孤立奇点。此外，如果X'是C 3 ，则p扩展到C 3 上的多项式，其在合适的坐标系中是线性的。这暗示了论文标题中阐述的事实。
Let X' be a complex affine algebraic threefold with H 3 (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 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. This implies the fact formulated in the title of the paper.