有理倒钩平面曲线与雅可比环的局部上同调

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2017-07-17 DOI:10.4171/cmh/471

A. Dimca

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引用次数: 15

摘要

本文给出了至少6次且只有加权齐次奇点的有理尖头平面曲线的完全投影分类。它还揭示了以前用Tjurina数描述自由曲线和近似自由曲线的一些新特征。最后，我们提出了Terao猜想的一种更强的形式，即线排列的自由度由其组合决定。

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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On rational cuspidal plane curves and the local cohomology of Jacobian rings

This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and nearly free curves in terms of Tjurina numbers. Finally, we suggest a stronger form of Terao’s conjecture on the freeness of a line arrangement being determined by its combinatorics.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.