基于加权爆破的数学解析
Algorithmic resolution via weighted blowings up
摘要：
在本文中，我们描述了一个计算机实现的阿布拉莫维奇，Temkin，和Wlodarczyk的算法解决奇点的特征零。他们的“加权分辨率”算法通过沿着独立于过去爆炸历史的中心重复爆炸来进行，将加权分辨率与以前的分辨率算法区分开来，后者都依赖于历史。我们将加权分辨率的实现与Villamayor的分辨率算法进行了比较，实验验证了加权分辨率的效率非常高。
英文摘要：
In this paper we describe a computer implementation of Abramovich, Temkin, and Wlodarczyk's algorithm for resolving singularities in characteristic zero. Their "weighted resolution" algorithm proceeds by repeatedly blowing up along centers that are independent of the history of the past blowing ups, distinguishing weighted resolution from previous resolution algorithms, which all rely on history. We compare our implementation of weighted resolution with that of Villamayor's resolution algorithm, experimentally verifying that weighted resolution is remarkably efficient.
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