论文标题
通过Frobenius结构定理比较非架构和对数镜子结构
Comparison of non-archimedean and logarithmic mirror constructions via the Frobenius structure theorem
论文作者
论文摘要
对于具有X \ d光滑仿射的原木calabi yau对（x，d），可以满足“规范壁结构和固有的镜子对称性”的假设1.1，或者包含一个Zariski密集的圆环，我们证明，我们在d的条件下，在nef的支持下，在nef的支持下，结构定义了镜像构造的量子，而始终是始终构造的统一的统一的统一统计的统一统治者，使统一的统一统计的统一统治统治统一的统一的统一范围。由Keel-Yu在“ frobenius结构定理的log calabi-yau品种中的定义1.1中”。作为推论，我们推断出由Gross-Siebert和Keel-yu在情况下构建的镜像代数的平等性，X \ d包含一个Zariski浓密的圆环。此外，我们使用此结果来证明曼德尔在“ Frobenius结构构想的Fano镜子周期”中提出的镜像猜想，以满足假设1.1的Fano对。
For a log Calabi Yau pair (X,D) with X\D smooth affine, satisfying either assumption 1.1 of "The canonical wall structure and intrinsic mirror symmetry" or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor, that the structure constants defining a trace form on the mirror algebra constructed by Gross-Siebert are given by the naive curve counts defined by Keel-Yu in definition 1.1 of "The Frobenius structure theorem for log Calabi-Yau varieties containing a torus". As a corollary, we deduce the equality of the mirror algebras constructed by Gross-Siebert and Keel-Yu in the case X\D contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel in "Fano mirror periods from the Frobenius structure conjecture" for Fano pairs satisfying assumption 1.1.
