Scattering diagrams, theta functions, and refined tropical curve counts
Scattering diagrams, theta functions, and refined tropical curve counts
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散点图、theta 函数和精确的热带曲线计数
DOI：
10.1112/jlms.12498
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Travis Mandel
中科院分区：
文献类型：
--
作者：
Travis Mandel
在Gross-Siebert镜像对称程序中，某些热带盘的计数被编码在称为散射图和虚线的组合对象中。这些，反过来，被用来构建一个镜像计划配备了一个规范的基础上，定期功能称为θ函数。本文旨在发展量子背景下热带盘、散射图和折线之间的关系;例如，我们用热带盘的精确计数来表示量子θ函数，并应用这些热带描述来证明Carl-Pumperla-Siebert的一个精确版本（预印本）结果的一致性θ函数，也证明了量子弗罗贝尼乌斯猜想的福克和贡恰洛夫（Ann.科学。等。诺姆上级(4)42（2009）865-930）。
In the Gross–Siebert mirror symmetry program, certain enumerations of tropical disks are encoded in combinatorial objects called scattering diagrams and broken lines. These, in turn, are used to construct a mirror scheme equipped with a canonical basis of regular functions called theta functions. This paper serves to develop the relationships between tropical disks, scattering diagrams, and broken lines in the quantum setting; for example, we express quantum theta functions in terms of refined enumerations of tropical disks.We apply these tropical descriptions to prove a refined version of the Carl–Pumperla–Siebert (Preprint) result on consistency of theta functions, and also to prove the quantum Frobenius Conjecture of Fock and Goncharov (Ann. Sci. Éc. Norm. Supér. (4) 42 (2009) 865–930).
利用热带几何形状进行精细曲线计数
影响因子：
1.8
作者：
Block F
通讯作者：
Block F