论文标题
准烟叶和稳定对
Quasimaps and stable pairs
论文作者
论文摘要
我们证明了$ y = \ y = \ Mathcal {a} _ {m-1} \ times \ times \ mathbb {c} $与$ y = \ mathcal {a} $ y Mathcal {a} $与quasimaps的理论与$ x = = \ m atrm {hilb {hilb}（$ mathcal的形式{a a a a a） k理论上的顶点。特别是，通过框计数明确描述了两个顶点的组合。然后，我们将等效性用于研究对$ y $ y $ y $的含义，这些理论是从3D镜像对称的准对象到$ x $的，包括唐纳森 - 托马斯·克雷普特分辨率的猜想。
We prove an equivalence between the Bryan--Steinberg theory of $π$-stable pairs on $Y = \mathcal{A}_{m-1} \times \mathbb{C}$ and the theory of quasimaps to $X = \mathrm{Hilb}(\mathcal{A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of both vertices are described explicitly via box counting. Then we apply the equivalence to study the implications for sheaf-counting theories on $Y$ arising from 3d mirror symmetry for quasimaps to $X$, including the Donaldson--Thomas crepant resolution conjecture.
