发表机构
Columbia University; University of California, Berkeley（哥伦比亚大学; 加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究从$\bbP^1$到中岛箭图簇$X$的有基拟映射模空间的临界上同调，构造其两个导出等价临界表示，得到典范DT层，证明移位杨代数与量子化库仑分支作用的相容性，猜想该结论普遍成立并归约为层论命题。
AI 中文摘要
本文系统研究从射影直线$\bbP^1$到中岛箭图簇$X$的有基拟映射的模空间$\text{QM}^{\boldsymbol{\text{ξ}}}(\bbP^1, X)$的临界上同调。我们构造该模空间作为整体临界轨迹的两个导出等价表示，据此得到该模空间的典范DT层的两个等价显式实现。利用每个临界表示，我们描述了移位杨代数和量子化库仑分支在拟映射临界上同调上的典范作用。我们通过几何方法构造了从适当霍尔代数到库仑分支的典范态射，并证明在额外假设下，我们描述的两个作用通过该态射相容。我们猜想该相容关系普遍成立，并将该断言归约为可通过乔伊斯猜想处理的层论命题。
英文摘要
This article presents a systematic study of the critical cohomology of $\QM^ξ(\bbP^1, X)$, the moduli space of based quasimaps from $\bbP^1$ to a Nakajima quiver variety $X$. We develop two derived equivalent presentations of this moduli space as a global critical locus. Accordingly, we obtain two equivalent explicit realizations of the canonical DT sheaf of the moduli space. Using each critical presentation, we describe canonical actions of shifted Yangians and quantized Coulomb branches on the quasimap critical cohomologies. We produce, by geometric means, a canonical morphism from an appropriate Hall algebra to the Coulomb branch, and show that the two actions we describe are compatible via this morphism under an additional hypothesis. We conjecture the compatibility holds generally, and reduce the claim to a sheaf-theoretic statement that may be approached via Joyce conjecture.
Comments239 pages, comments welcome!
