Nash trivial simultaneous resolution for a family of zero-sets of Nash mappings
Nash trivial simultaneous resolution for a family of zero-sets of Nash mappings
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纳什映射零集族的纳什平凡联立解析
DOI：
10.1007/s002099900109
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发表时间：
2000
影响因子：
0.8
通讯作者：
S. Koike
中科院分区：
文献类型：
--
作者：
S. Koike
研究了真实的多项式映射或Nash映射的零集族的平凡性。那么，很自然地要问有限分类定理对于平凡性是否成立。在解释本文的结果之前，我们回顾一下纳什流形和纳什映射的定义。欧氏空间Rm的解析子流形M称为纳什流形，如果它在Rm中是半代数的。在本文中，子流形总是指正则子流形。一个解析映射f：M→ N，其中M <$Rm和N <$Rn是Nash流形，如果f的图在Rm× Rn中是半代数的，则称f为Nash映射。我们进一步称纳什映射的零集为纳什集。对于一族代数集或Nash集，有限性定理已经建立在拓扑平凡性上（T。Fukuda [7]，AN Varcenko [31]），更强烈地，在半代数平凡（RM Hardt [11]）。这里我们考虑以下问题：
We consider triviality of a family of zero-sets of real polynomial mappings or Nash mappings. Then it is natural to ask whether a finite classification theorem holds or not for the triviality. Before explaining the results in this paper, we recall the definitions of a Nash manifold and a Nash mapping. An analytic submanifold M of some Euclidean space Rm is called a Nash manifold, if it is semialgebraic in Rm. In this paper, a submanifold always means a regular submanifold. An analytic mapping f: M→ N, where M⊂ Rm and N⊂ Rn are Nash manifolds, is called a Nash mapping, if the graph of f is semialgebraic in Rm× Rn. We further call the zero-set of a Nash mapping a Nash set. For a family of algebraic sets or Nash sets, finiteness theorems have been established on topological triviality (T. Fukuda [7], AN Varcenko [31]) and, more strongly, on semialgebraic triviality (RM Hardt [11]). Here we consider the following problem: