$\mathbb｛P｝^2的热带超势$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-03-22 DOI:10.14231/ag-2020-002

T. Prince

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引用次数: 3

摘要

我们给出了Carl-Pumperla-Siebert所考虑的热带超势计算的一个扩展实例。特别地，我们考虑了与非奇异亏格一平面曲线的补相关的仿射流形，并计算了由Gross-Sibert算法确定的壁和室分解。利用Carl-Pumperla-Siebert的结果，我们通过虚线计数确定了分解过程中每个腔室中的热带超势。超势在每个腔中定义了一个Laurent多项式，我们证明它与Coates-Corti-Galkin-Golyshev-Kaspzryk预测的Laurent多项式相同，是$\mathbb｛P｝^2$的镜像。

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The tropical superpotential for $\mathbb{P}^2$

We present an extended worked example of the computation of the tropical superpotential considered by Carl--Pumperla--Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve, and calculate the wall and chamber decomposition determined by the Gross--Siebert algorithm. Using the results of Carl--Pumperla--Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, which we demonstrate to be identical to the Laurent polynomials predicted by Coates--Corti--Galkin--Golyshev--Kaspzryk to be mirror to $\mathbb{P}^2$.

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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.