论文标题
家庭浮动计划和非架构的syz镜面构造
Family Floer program and non-archimedean SYZ mirror construction
论文作者
论文摘要
鉴于拉格朗日的振动，我们提供了镜像Landau-Ginzburg模型的自然结构，该模型由刚性的分析空间，超电势函数和基于福卡亚的家庭浮子理论的双振动组成。 B侧中的镜像是由A侧的Holomorthic Disk的计数以及非架构分析和$ A_ \ infty $结构的同源代数构建的。它与SYZ双振动图片非常吻合，并解释了量子/激体校正和墙壁交叉现象。我们只需要假设较弱的半阳性拉格朗日振动即可进行非固定的syz镜像重建，而不是特殊的拉格朗日纤维化。
Given a Lagrangian fibration, we provide a natural construction of a mirror Landau-Ginzburg model consisting of a rigid analytic space, a superpotential function, and a dual fibration based on Fukaya's family Floer theory. The mirror in the B-side is constructed by the counts of holomorphic disks in the A-side together with the non-archimedean analysis and the homological algebra of the $A_\infty$ structures. It fits well with the SYZ dual fibration picture and explains the quantum/instanton corrections and the wall crossing phenomenon. Instead of a special Lagrangian fibration, we only need to assume a weaker semipositive Lagrangian fibration to carry out the non-archimedean SYZ mirror reconstruction.
