Nested sets and Jeffrey Kirwan cycles

Equivariant Jeffrey-Kirwan localization theorem in non-compact setting

We generalize the Jeffrey-Kirwan localization theorem for non-compact symplectic and hyperKahler quotients. Similarly to the circle compact integration of Hausel and Proudfoot we define equivariant integrals on non-compact manifolds using the Atiyah-Bott-Berline-Vergne localization formula as formal definition. We introduce a so called equivariant Jeffrey-Kirwan residue and we show that it shares similar properties as the usual one. Our localization formula has the same structure as the usual Jeffrey-Kirwan formula, but it uses formal integration and equivariant residue. We also give a version…

散射图与Jeffrey-Kirwan留数

Scattering diagrams and Jeffrey-Kirwan residues

本文利用Maurer-Cartan渐近分析，证明了初始散射图的一致完全化及其theta函数可由显式亚纯形式的Jeffrey-Kirwan留数表示。

对数 Calabi–Yau 曲面与 Jeffrey–Kirwan 残数

Log Calabi-Yau surfaces and Jeffrey-Kirwan residues

本文证明无环无有向圈箭图相关亚纯形式的 Jeffrey–Kirwan 残数等于其 Donaldson–Thomas 型不变量，并在完全二部箭图情形借助散射图与 theta 函数说明其由 Gross–Hacking–Keel 镜像族确定。

虚拟杰弗里 - 柯万局部化

Virtual Jeffrey--Kirwan localisation

研究如何根据固定点集\(X^T\)的虚拟周期积分表示GIT商\(X/\!\!/G\)的虚拟周期积分，适用于多种理论和结构，以及非紧致德莱格 - 芒福德层。

四维Pandharipande-Thomas顶点与Jeffrey-Kirwan残差

The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue

本文提出一种轮廓积分方法计算四维K理论equivariant Pandharipande-Thomas顶点，并展示通过选择不同参考向量可将该顶点与Donaldson-Thomas顶点关联。通过曲线和曲面示例，探讨了四维设定下的DT/PT对应关系及其高阶和超群推广。

来自 Jeffrey-Kirwan 留数的晶体与双重箭图代数

Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues

本文构建了描述超对称箭图规范理论 Witten 指标的晶体熔化模型，基于 Jeffrey-Kirwan 留数将其推广至无重叠条件箭图，并提出双重箭图代数以描述 BPS 态。