论文标题
在窗口定理上，用于本地表面及其应用的分类唐纳森 - 托马斯理论
On window theorem for categorical Donaldson-Thomas theories on local surfaces and its applications
论文作者
论文摘要
在本文中，我们证明了本地表面上的分类Donaldson-Thomas理论的窗口定理，作为GIT商堆栈窗口定理的类似物。我们给出了我们主要结果的两个应用。第一个是在某些技术条件下，在严格的半固定滑轮上，在本地表面上，DT类别的壁缝等效的证明。第二个是在减少曲线类时，显示从分类PT理论到分类MNOP理论的完全信仰函子的存在。这些结果表明数值DT不变性的壁划入公式的分类，并且也被认为是Birational几何形状中D/K构想的D-临界类似物。
In this paper, we prove a window theorem for categorical Donaldson-Thomas theories on local surfaces as an analogue of window theorem for GIT quotient stacks. We give two applications of our main result. The first one is a proof of wall-crossing equivalences of DT categories for one dimensional stable sheave on local surfaces, under some technical condition on strictly semistable sheaves. The second one is to show the existence of fully-faithful functors from categorical PT theories to categorical MNOP theories, when the curve class is reduced. These results indicate categorifications of wall-crossing formulas of numerical DT invariants, and also regarded as d-critical analogue of D/K conjecture in birational geometry.
