论文标题
符号表面和固定基因座的模仿空间的固定基因座类别
Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
论文作者
论文摘要
给定有限的组$ g $在流畅的投射品种$ x $的派生类别中的作用，我们将$ d^b（\ mathrm {coh}（x）$中稳定对象的诱导$ g $ action的固定基因座与稳定对象的稳定对象的固定位置与ecoriant of ecrovariant类别中的Moduli space的稳定对象相关联。 $ d^b（\ mathrm {coh}（x））_ g $。作为应用程序，我们获得了在符号表面的派生类别上的符号动作类别的标准，以等同于表面的派生类别。这概括了派生的McKay对应关系，并产生了一个通用框架，用于描述在符号表面上稳定对象的模量空间上的固定基因座。
Given an action of a finite group $G$ on the derived category of a smooth projective variety $X$ we relate the fixed loci of the induced $G$-action on moduli spaces of stable objects in $D^b(\mathrm{Coh}(X))$ with moduli spaces of stable objects in the equivariant category $D^b(\mathrm{Coh}(X))_G$. As an application we obtain a criterion for the equivariant category of a symplectic action on the derived category of a symplectic surface to be equivalent to the derived category of a surface. This generalizes the derived McKay correspondence, and yields a general framework for describing fixed loci of symplectic group actions on moduli spaces of stable objects on symplectic surfaces.
