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摘要翻译：
本文在代数集的代数族中引入了与相容过滤相一致的blow-半代数平凡性的概念，作为实代数奇点的等性。给出一个定义在非奇异代数簇上的三维代数集的代数族，我们证明了参数代数集在连通Nash流形上存在一个有限的剖分，在这个剖分上，该族允许一个符合相容过滤的blow-semialgebridation。通过Artin-Mazur定理，我们对三维Nash集族也给出了类似的有限性结果。作为证明中论据的推论，我们得到了一个关于从二维欧氏空间到p-双欧氏空间的多项式映射的半代数类型的有限性定理。
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英文标题：
《Finiteness theorem on Blow-semialgebraic triviality for a family of
3-dimensional algebraic sets》
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作者：
Satoshi Koike
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper we introduce the notion of Blow-semialgebraic triviality consistent with a compatible filtration for an algebraic family of algebraic sets, as an equisingularity for real algebraic singularities. Given an algebraic family of 3-dimensional algebraic sets defined over a nonsingular algebraic variety, we show that there is a finite subdivision of the parameter algebraic set into connected Nash manifolds over which the family admits a Blow-semialgebraic trivialisation consistent with a compatible filtration. We show a similar result on finiteness also for a Nash family of 3-dimensional Nash sets through the Artin-Mazur theorem. As a corollary of the arguments in their proofs, we have a finiteness theorem on semialgebraic types of polynomial mappings from the 2-dimensional Euclidean space to the p-diemnsional Euclidean space.
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PDF链接：
https://arxiv.org/pdf/0711.2862
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