五次三维簇的锥形间隙

中文摘要 AI 辅助

我们证明了五次三维簇、其他光滑费马卡拉比-丘三维簇超曲面以及局部$\mathbb P^2$的Gromov--Witten（GW）理论，以及与这些超曲面相关的FJRW理论的全亏格锥形间隙猜想。我们的证明使用了混合自旋P场（MSP）理论和类似的master-space构造。核心对象是\emph{锥-顶点理论}。我们将该理论通过形式拉普拉斯变换表示为点CohFT的平移，并证明了所得平移理论的普适锥形间隙定理。随后，master-space构造将间隙从锥-顶点理论转移到GW和FJRW理论。

英文摘要

We prove the all-genus conifold gap conjecture for the Gromov--Witten (GW) theories of the quintic threefold, other smooth Fermat Calabi--Yau threefold hypersurfaces, and local $\mathbb P^2$, as well as for the FJRW theories associated with these hypersurfaces. Our proof uses Mixed Spin P-field (MSP) theory and analogous master-space constructions. The central object is the \emph{cone-vertex theory}. We express this theory as a translation of the point CohFT via a formal Laplace transform and prove a universal conifold gap theorem for the resulting translated theories. The master-space construction then transfers the gap from the cone-vertex theory to the GW and FJRW theories.

发表机构

• Institute for Math and AI & School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
• School of Mathematical Sciences, Peking University（北京大学数学科学学院）
• Great Bay University, Great Bay Institute for Advanced Study（大湾区大学前沿高等研究院）

机构由 AI 辅助整理，请以论文原文为准。