Resolution of singularities of an idealistic filtration in dimension 3 after Benito-Villamayor
Resolution of singularities of an idealistic filtration in dimension 3 after Benito-Villamayor
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Benito-Villamayor 之后 3 维理想主义过滤奇点的解析
DOI：
10.2969/aspm/07010115
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
K. Matsuki
中科院分区：
文献类型：
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作者：
Hiraku Kawanoue;K. Matsuki
我们将Benito-Villamayor最近发展的方法融入到我们的框架中，建立了一个求解三维(局部水平)正特征理想渗流奇异性的算法。虽然我们的算法(全局版本)只暗示了曲面在3维光滑环境空间中的嵌入分辨率，这是一个已知的经典结果，但我们引入了一些新的不变量，它有效地衡量了在算法过程中奇异性得到了多少改进，并且在每次爆炸后严格地下降了。这与众所周知的Abhyankar-Moh病理相反，即在爆炸下残留顺序增加和Hauser观察到的“袋鼠”点现象。
We establish an algorithm for resolution of singularities of an idealistic filtration in dimension 3 (at the local level) in positive characteristic, incorporating the method recently developed by Benito-Villamayor into our framework. Although (a global version of) our algorithm only implies embedded resolution of surfaces in the smooth ambient space of dimension 3, a classical result known before, we introduce some new invariant which effectively measures how much singularities are improved in the process of our algorithm and which strictly drops after each blow up. This is in contrast to the well-known Abhyankar-Moh pathology of the increase of the residual order under blow up and the phenomenon of the "Kangaroo" points observed by Hauser.