关于有界负性猜想与奇异平面曲线

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2021-01-18 DOI:10.17323/1609-4514-2022-22-3-427-450

A. Dimca, Gabriel Sticlaru

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引用次数: 0

摘要

我们证明了Brian Harbourne提出的关于有界负性猜想和奇异平面曲线的两个问题在某些情况下有一个负的答案。对于只有普通奇点的有理曲线，这个问题被证明与这种曲线可能具有的大于或等于3倍的奇点数目的强新界限有关。这一事实提出了一个关于只有普通三点作为奇点的有理曲线不存在的猜想。我们也给出了H常数H(C)的下界，根据C的奇点的最大多重性，或者当C只有1≤s≤5和D4的a型奇点时。

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On the Bounded Negativity Conjecture and Singular Plane Curves

We show that two questions raised by Brian Harbourne related to the bounded negativity conjecture and singular plane curves have a negative answer in some cases. For rational curves having only ordinary singularities, this question is shown to be related to strong new bounds on the number of singularities of multiplicity greater or equal to 3 such a curve may have. This fact suggests a conjecture on the non-existence of rational curves of degree d > 8 having only ordinary triple points as singularities. We also give lower bounds for theH-constant H(C) in terms of the maximal multiplicity of the singularities of C, or when C has only singularities of type As with 1 ≤ s ≤ 5 and D4.

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.