Patching local uniformizations
Patching local uniformizations
复制标题
修补局部统一
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
O. Villamayor
中科院分区：
文献类型：
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作者：
Scientifiques DE L’É.N.S;O. Villamayor
. - 在[VI]中，我们介绍了一个典型的算法解决奇异性的特征零（见第8节，本文明确的例子）。这证明了构造！分解定理的存在性。本文的新奇在于综合定义了格罗夫斯和格罗夫斯上的函数。事实上，我们能够给一个几乎自成一体的帐户的主要方面的决议的奇异性，详细介绍的结果在[六]，也包括一个证明解除集团行动的计划，其建设性的决议。同时，本文强烈关注算法本身，以激励显式计算。正则概型的约化子概型的奇异性的嵌入分解由该子概型的奇异性的分解以及最终结果与由该过程引入的例外超曲面的法向相交的条件组成。这个过程，在术语上，可以表示为一个中间“决议”的串联称为格罗夫斯的决议。在第8节中，我们举例说明了群作用的分解和提升，并讨论了我们对奇异点的算法（或建设性）分解的自然结果：局部一致化的修补。
. - In [Vi] we introduced a canonical algorithm for resolution of singularities in characteristic zero (see section 8 of this paper for explicit examples). This proved the construct! veness of the theorem of resolution. The novelty in this paper is a synthetic definition of groves and a notion of funtions on groves. Indeed we are able to give an almost selfcontained account of main aspects of resolution of singularities, a detailed presentation of the results in [Vi] and also to include a proof of the lifting of group actions on a scheme to its constructive resolution. At the same time this paper is strongly focused on the algorithm itself as to motivate explicit computations. An embedded resolution of singularities of a reduced subscheme of a regular scheme consists of a resolution of singularities of the subscheme together with a condition of normal crossings of the final outcome with the exceptional hypersurfaces introduced by this procedure. This process, in terms, can be expressed as a concatenation of intermediate "resolutions" called resolutions of groves. In section 8 we exemplify both, resolutions and lifting of group actions and discuss a natural outcome of our algorithmic (or constructive) resolution of singularities: the patching of local uniformizations.