On $$\nu $$ -Quasiordinary Surface Singularities and Their Resolution

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-05 DOI:10.1007/s00009-024-02709-x

Fuensanta Aroca, José M. Tornero

引用次数: 0

Abstract

Quasiordinary power series were introduced by Jung at the beginning of the 20th century, and were not paid much attention until the work of Lipman and, later on, Gao. They have been thoroughly studied since, as they form a very interesting family of singular varieties, whose properties (or at least many of them) can be encoded in a discrete set of integers, much as what happens with curves. Hironaka proposed a generalization of this concept, the so-called $\nu $-quasiordinary power series, which has not been examined in the literature in such detailed way. This paper explores the behavior of these series under the resolution process in the surface case.

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论 $$\nu $$ - 准奇异面奇点及其解析

准平凡幂级数是荣格在 20 世纪初提出的，直到利普曼和后来的高晓松的研究才引起人们的注意。此后，人们对它们进行了深入研究，因为它们构成了一个非常有趣的奇异品种族，其性质（或至少其中的许多性质）可以用离散的整数集来编码，就像曲线一样。Hironaka 提出了这一概念的广义化，即所谓的 $\nu $-准平凡幂级数，但文献中还没有对它进行如此详细的研究。本文探讨了这些序列在曲面情况下的解析过程中的行为。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.