论文标题
在亚分析集的全球平滑度上
On the degree of global smoothings for subanalytic sets
论文作者
论文摘要
在[4]中，Bierstone和Parusinski证明了封闭的亚分析集的全球平滑性，无论是在嵌入式和非安装意义上。特别是，在未填充的降低过程中，作者构建了（通常）均匀程度的平滑，确实是众所周知的亚分析集的存在，这些集合的存在不承认（通常）奇数程度的未填充平滑。在本文中，我们为亚分析集引入了一种自然拓扑概念，我们证明了一个标准来确定封闭的亚分析集$ x $是否仅接受沿着非结合赤道的全球平滑度。详细介绍，我们证明，如果$ x $具有不符合的赤道$ y $，则每次平滑$ x $，这是连接的社区$ w $ $ y $的覆盖，甚至超过$ W $。
In [4] Bierstone and Parusinski proved the existence of global smoothings for closed subanalytic sets, both in an embedded and a non-embedded sense. In particular, in the non-embedded desingularization procedure the authors construct smoothings of (generically) even degree, indeed it is well-known the existence of subanalytic sets which do not admit non-embedded smoothings of (generically) odd degree. In this paper we introduce a natural topological notion of nonbounding equator for subanalytic sets and we prove a criterion to determine whether a closed subanalytic set $X$ only admits global smoothings of even degree along the nonbounding equator. More in detail, we prove that if $X$ has a nonbounding equator $Y$ then every smoothing of $X$ which is a covering on a connected neighborhood $W$ of $Y$ has even degree over $W$.
