由Maurer-Cartan方程渐近分析得到的散射图
代数几何
2022-02-23 v2 数学物理
math.MP
辛几何
摘要
设\check{X}_0为一个半平坦Calabi-Yau流形,配备有拉格朗日环面纤维化\check{p}:\check{X}_0 \rightarrow B_0。我们遵循Fukaya于2005年提出的纲领,通过将\check{X}_0上的Kodaira-Spencer形变理论的Maurer-Cartan解沿\check{p}在B_0中可缩开子集U上的纤维展开为傅里叶级数,来研究其渐近行为。我们证明,一类特定Maurer-Cartan解的傅里叶模式的半经典极限(即渐近展开中的首项)自然给出一致的散射图,散射图是热带组合对象,在Kontsevich-Soibelman和Gross-Siebert关于镜像对称重构问题的研究中起到了关键作用。
引用
@article{arxiv.1807.08145,
title = {Scattering diagrams from asymptotic analysis on Maurer-Cartan equations},
author = {Kwokwai Chan and Naichung Conan Leung and Ziming Nikolas Ma},
journal= {arXiv preprint arXiv:1807.08145},
year = {2022}
}
备注
54 pages, 17 figures; v2: significantly shortened because the preliminary materials (Sections 2 and 3) have been made much more concise (see the survey article arXiv:1811.09042 for more background) and Section 6, the main result of which basically follows directly from previous sections, has been removed (and will be appear elsewhere); all the main results and their proofs remain unchanged