量子指标、阿诺德 - 罗赫林曲面与实枚举几何
Quantum index, Arnold-Rokhlin surfaces, and real enumerative geometry
AI总结：
研究关联用于定义复曲面实枚举不变量的两种韦尔申格型符号规则，其关系涉及量子指标与实曲线点集几何，还提出量子指标新定义用于非复曲面实代数曲线精细不变量枚举。
AI中文摘要：
本笔记的主要目标是关联用于定义复曲面实枚举不变量（所考虑的不变量相对于复曲面边界）的两种不同的韦尔申格型符号规则。它们之间的关系将米哈伊尔金的量子指标与所计数实曲线的实点集和复点集的几何联系起来。作为副产品，我们提出了量子指标的新定义，可用于非复曲面设置下实代数曲线的精细不变量枚举。
英文摘要：
The main goal of this note is to relate two different Welschinger-type rules of signs that were used for definition of real enumerative invariants of toric surfaces (the invariants considered being relative to the toric boundary). The relation between them intertwines Mikhalkin's quantum index and geometry of real and complex point sets of counted real curves. As a by-product, we suggest a new definition of quantum index, which can be used for refined invariant enumeration of real algebraic curves on surfaces in a non-toric setup.
