Functorial embedded resolution via weighted blowings up

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-09-18 DOI:10.2140/ant.2024.18.1557

Dan Abramovich, Michael Temkin, Jarosław Włodarczyk

引用次数: 0

Abstract

We provide a simple procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history, no exceptional divisors, and no logarithmic structures are necessary to carry this out; the steps are explicit geometric operations requiring no choices; and the resulting algorithm is efficient.

A similar result was discovered independently by McQuillan (2020).

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通过加权吹胀的函数式嵌入解析

我们提供了一个简单的程序，在特征 0 中，通过堆栈理论意义上的加权炸毁，反复炸毁最差的奇点，来解决嵌入光滑变种 Y 中的变种 X 的奇点。要做到这一点，不需要历史，不需要特殊除数，也不需要对数结构；这些步骤都是明确的几何运算，不需要任何选择；所得到的算法是高效的。麦奎伦（2020）也独立发现了类似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.