论文标题
刺穿的对数R-MAP
Punctured logarithmic R-maps
论文作者
论文摘要
在本文中，我们将刺穿的R-MAP的理论发展为对数测量线性Sigma模型（Log GLSM）的关键组成部分。从ACG的意义上讲，刺穿的R-MAP是一张刺穿的地图，进一步由域曲线上的差速器捆扎。他们承认了两种不同但密切相关的完美障碍理论 - 一种规范性的理论和一种缩小的理论。尽管规范理论导致具有目标和旋转结构的普遍双重分析循环，但没有扩展，但降低的理论描述了对数GLSM中的边界贡献。 本文的主要结果包括规范和简化理论中的一系列公理： 1。根据连接的产品公式计算不变的不变性 2。基本的班级公理，弦和除数方程 作为重要的应用，这些公式导致了降低理论中的一类不变性，称为有效不变。它们是GW理论最新进展的核心，并将证明在高级GW理论中为量子Lefschetz原理产生明确的校正条款，以在即将到来的论文中为任意平滑的完整交集。 对于五重的3倍，我们表明所有有效的不变性均由$ [（2G-2）/5] + 1 $使用（1）和（2）中的公式确定。这符合著名的BCOV B-Model理论的自由参数的数量。类似的结果适用于其他完整的交叉点。这与最后两位作者的联合作品和S. guo在属属中的定理和五五倍的较高属镜子构想中，这表明log glsm是证明高等GW属理论中BCOV型猜想的有效工具。 刺穿的R-MAP的进一步应用包括有效不变剂的LG/CY对应关系以及与全态差异基因座的关系。
In this paper, we develop the theory of punctured R-maps as a crucial component of logarithmic gauged linear sigma models (log GLSM). A punctured R-map is a punctured map in the sense of ACGS, further twisted by the sheaf of differentials on the domain curve. They admit two different but closely related perfect obstruction theories - a canonical one and a reduced one. While the canonical theory leads to generalized double ramification cycles with targets and spin structures, without expansions, the reduced theory describes boundary contributions in log GLSM. Major results of this paper include a sequence of axioms in both canonical and reduced theories: 1. A product formula computing disconnected invariants in terms of connected ones 2. Fundamental class axioms, string and divisor equations As an important application, these formulas lead to a class of invariants in the reduced theory, called effective invariants. They are at the heart of recent advances in GW theory, and will be shown to give rise to explicit correction terms to the quantum Lefschetz principle in higher genus GW theory for arbitrary smooth complete intersections in a forthcoming paper. For quintic 3-folds, we show that all effective invariants are determined by $[(2g-2)/5] + 1$ many basic effective invariants, using the formulas in (1) and (2). This matches the number of free parameters of the famous BCOV B-model theory in physics. Similar results apply to other complete intersections. This, together with the joint works of the last two authors and S. Guo on the genus two mirror theorem and the higher genus mirror conjectures for quintic 3-folds, shows that log GLSM is an effective tool for proving BCOV-type conjectures in higher genus GW theory. Further applications of punctured R-maps include an LG/CY correspondence for effective invariants and a relation to the locus of holomorphic differentials.
