通过Pandharipande ` ` Pixton ` ` Zvonkine $r$-自旋关系的$\mathcal{M}_{g,n}$的重言环

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-03-02 DOI:10.14231/AG-2018-019

Reinier Kramer, Farrokh Labib, D. Lewanski, S. Shadrin

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引用次数: 4

摘要

利用Pandharipande、Pixton和Zvonkine从r-自旋Witten类的给定公式中导出的模空间Mg,n的重言环上的关系，得到开模空间Mg,n的重言环的维数限制。特别地，我们给出了关于luijenga(对于n = 1)和Buryak等人(对于n bb> 2) dimRg-1(Mg,n)≤n的新证明。我们也给出了关于luijenga(对于n = 1)和Ionel(对于任意n bb> 1)对于i bb> g Ri(Mg,n) = 0的新证明，并给出了Ri(Mg,n)在i≤g- 2时的维数估计。

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The tautological ring of $\mathcal{M}_{g,n}$ via Pandharipande�Pixton�Zvonkine $r$-spin relations

We use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spacesMg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg-1(Mg,n) ≤ n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i ≤ g - 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.