论文标题
库尔 - 托马斯不变的细化，通过$ k $ - 理论不变性
Refinements of Kool-Thomas Invariants via Equivariant $K$-theoretic invariants
论文作者
论文摘要
在本文中，我们将通过Nekrasov和Okounkov提出的Equivariant $ k $不变性来定义本地表面的Kool-Thomas不变性。库尔（Kool）和托马斯（Thomas）将稳定对模量的障碍理论定义为$ \ nathcal {p}_χ（x，i _ {*}β）$的障碍理论，为虚拟类别$ \ left [\ nathcal {p}_χ（p}_χ（s，β）\ righ]^$的虚拟级别$ \ weft [\ nathcal {p} _} $） H^{*}（\ Mathcal {p}_χ（x，i _ {*}β），\ mathbb {z}）$。 $τ（[pt]）$包含一个点的发病率和支持$（\ Mathcal {f}，s）$的曲线。 $ \ textbf {关键字：} $ kool-thomas不变性，$ k $ - 理论不变性，göttscheshende norvariants
In this article we are defining a refinement of Kool-Thomas invariants of local surfaces via the equivariant $K$-theoretic invariants proposed by Nekrasov and Okounkov. Kool and Thomas defined the reduced obstruction theory for the moduli of stable pairs $\mathcal{P}_χ(X,i_{*}β)$ as the degree of the virtual class $\left[\mathcal{P}_χ(S,β)\right]^{red}$ after we apply $τ([pt])^{m}\in H^{*}(\mathcal{P}_χ(X,i_{*}β),\mathbb{Z})$. $τ([pt])$ contain the information of the incidence of a point and a curve supporting a $(\mathcal{F},s)$. $\textbf{Keywords: }$Kool-Thomas invariants, $K$-theoretic invariants, Göttsche Shende invariants
