Abstract:We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based on work by Cossart-Jannsen-Saito, though our variant uses a refinement of the order instead of the Hilbert-Samuel function as a measure for the complexity of the singularity. We particularly focus on aspects arising when working in mixed characteristics. Furthermore, we exploit the algorithm’s natural parallel structure rephrasing it in terms of Petri nets for use in the parallelization environment GPI-Space with Singular as computational back-end.

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中文翻译：

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针对算术曲面的嵌入式反丁香化–走向并行实现

摘要：考虑到可实现性，我们提出了一种算术表面的算法嵌入式去奇化处理。我们的算法基于Cossart-Jannsen-Saito的工作，尽管我们的变体使用阶数的细化代替Hilbert-Samuel函数来衡量奇异性的复杂性。我们特别关注在混合特性中出现的方面。此外，我们利用Petri网改写了算法的自然并行结构，将其改写为在并行化环境GPI-Space中使用奇异作为计算后端。

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