Towards the Classification of Semistable Fibrations Having Exactly Five Singular Fibers

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-19 DOI:10.1007/s00009-024-02667-4

Margarita Castañeda-Salazar, Margarida Mendes Lopes, Alexis Zamora

引用次数: 0

Abstract

Let X be a nonsingular complex projective surface. Given a semistable non isotrivial fibration \(f: X \rightarrow \mathbb {P}^{1}\) with general non-hyperelliptic fiber of genus \(g\ge 4\), we show that, if the number of singular fibers is 5, then \(g\le 11\), thus improving the previously known bound \(g\le 17\). Furthermore, we show that, for each possible genus, the general fiber has gonality at most 5. The corresponding fibrations are described as the resolution of concrete pencils of curves on minimal rational surfaces.

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对恰好有五条奇异纤维的半稳态纤变进行分类

让 X 是一个非星状复投影面。给定一个半稳态的非等阶纤维（f: X \rightarrow \mathbb {P}^{1}），其一般非椭圆纤维的属（g\ge 4\），我们证明，如果奇异纤维的数量是5，那么（g\le 11\），从而改进了之前已知的约束（g\le 17\）。此外，我们还证明，对于每一种可能的属，一般纤维都最多有 5 个冈性。相应的纤维被描述为极小有理曲面上曲线的具体铅笔的解析。

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.