开放式 $r$ 自旋不变式的镜像对称性

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI:10.4310/pamq.2024.v20.n2.a9

Mark Gross, Tyler L. Kelly, Ran J. Tessler

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引用次数: 0

摘要

我们证明，开放式 $r$ 自旋枚举不变式的生成函数产生了多项式 $x^r$ 的普遍展开。此外，参数化这一普遍展开的坐标是通过 Saito-Givental 理论与兰道-金兹堡模型 $(\mathbb{C}, x^r)$ 相关联的弗罗贝尼斯流形上的平坐标。这一结果为在更高维度出现同样现象提供了证据，并在续集 $\href{https://arxiv.org/abs/2203.02435}{[\textrm{GKT}22]}$ 中得到证明。

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Mirror symmetry for open $r$-spin invariants

We show that a generating function for open $r$-spin enumerative invariants produces a universal unfolding of the polynomial $x^r$. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau–Ginzburg model $(\mathbb{C}, x^r)$ via Saito–Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel $\href{https://arxiv.org/abs/2203.02435}{[\textrm{GKT}22]}$.

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.