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

IF 1.7 1区数学 Q1 MATHEMATICS

Algebraic Geometry 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

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.