曲面自等价的分类熵与拓扑熵

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2019-09-06 DOI:10.17323/1609-4514-2021-21-2-401-412

Dominique Mattei

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引用次数: 8

摘要

本文给出了包含(-2)-曲线的任意曲面具有正分类熵(在Dimitrov, Haiden, Katzarkov和Kontsevich意义上)的自等价的一个例子。然后我们证明了这个等价给出了Kikuta和Takahashi提出的一个猜想的另一个反例。在第二部分，我们研究了S表面上由标准自等价组成的球面扭转对上同调的作用，并证明了它们的谱半径对应于S的相应自同构的拓扑熵。

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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Categorical vs Topological Entropy of Autoequivalences of Surfaces

In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a (-2)-curve. Then we show that this equivalence gives another counter-example to a conjecture proposed by Kikuta and Takahashi. In a second part, we study the action on cohomology induced by spherical twists composed with standard autoequivalences on a surface S and show that their spectral radii correspond to the topological entropy of the corresponding automorphisms of S.

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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.