论文标题
排名$ n $ vafa-witten不变性，模块化和爆炸
Rank $N$ Vafa-Witten invariants, modularity and blow-up
论文作者
论文摘要
我们为精制的VAFA-WINTINERS $ω（γ，y）的生成功能提供了明确的表达，$ \ Mathbb {p}^2 $的任意等级$ n $的生成函数以及其非固态模块化完成。在推导过程中，我们还提供了：i）最近发现的$ω（γ，y）$的概括及其在模量空间的典范室内的Hirzebruch和Del Pezzo表面的完成概括到通用室； ii）爆炸公式的一个版本直接根据这些生成功能及其以明显的模块化形式进行重新制定。
We derive explicit expressions for the generating functions of refined Vafa-Witten invariants $Ω(γ,y)$ of $\mathbb{P}^2$ of arbitrary rank $N$ and for their non-holomorphic modular completions. In the course of derivation we also provide: i) a generalization of the recently found generating functions of $Ω(γ,y)$ and their completions for Hirzebruch and del Pezzo surfaces in the canonical chamber of the moduli space to a generic chamber; ii) a version of the blow-up formula expressed directly in terms of these generating functions and its reformulation in a manifestly modular form.
