论文标题
当地Syz奇点的家庭漂浮镜空间
Family Floer mirror space for local SYZ singularities
论文作者
论文摘要
我们在镜子太空对之间进行了数学上精确的SYZ猜想，并证明了与毛lagrangian Gross Lagrangian纤维化的任何曲折的Calabi-yau歧管。迄今为止，这是我们第一次意识到Syz提案，其唯一纤维超出了拓扑水平。双重奇异振动是明确编写的，并被证明与家庭浮光镜结构兼容。此外，我们发现，奇异拉格朗日的Maurer-Cartan集只是相应的双单数纤维的严格子集。这对先前的期望产生了负面的反应，并导致了Syz奇点的新观点。作为额外的证据，我们还检查了Landau-Ginzburg模型的众所周知的民俗猜想的一些计算。
We give a mathematically precise statement of the SYZ conjecture between mirror space pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To date, it is the first time we realize the SYZ proposal with singular fibers beyond the topological level. The dual singular fibration is explicitly written and proved to be compatible with the family Floer mirror construction. Moreover, we discover that the Maurer-Cartan set of a singular Lagrangian is only a strict subset of the corresponding dual singular fiber. This responds negatively to the previous expectation and leads to new perspectives of SYZ singularities. As extra evidence, we also check some computations for a well-known folklore conjecture for the Landau-Ginzburg model.
