论文标题
定位虚拟结构滑轮几乎完美的阻塞理论
Localizing Virtual Structure Sheaves for Almost Perfect Obstruction Theories
论文作者
论文摘要
作者在早期论文中引入了几乎完美的障碍理论，作为适当的概念，以定义虚拟结构皮带纸巾和$ k $的$ k $ - 理论不变式，用于许多感兴趣的模型堆栈，包括$ k $ - 理论的唐纳森 - 托马斯 - 托马斯 - 托马斯 - 托马斯不变的冰淇淋和calabi-yau yau thifolds上的冰淇淋和复合体。虚拟结构或骨的构造基于$ K $ - 理论和捆堆的吉森地图。 在本文中，我们将虚拟的圆环定位和安装本地化公式及其结合概括为几乎完美的阻塞理论的设置。为此，我们进一步研究了$ K $ - 捆堆及其功能性属性的理论。作为本地化公式的应用，我们为简单的$ \ Mathbb {c}^\ ast $ - wall杂交和定义$ k $ - $ k $不变性的不变式建立了$ k $ - 理论墙交叉公式，以完善jiang-thomas thomas thomas虚拟签名的欧拉特征。
Almost perfect obstruction theories were introduced in an earlier paper by the authors as the appropriate notion in order to define virtual structure sheaves and $K$-theoretic invariants for many moduli stacks of interest, including $K$-theoretic Donaldson-Thomas invariants of sheaves and complexes on Calabi-Yau threefolds. The construction of virtual structure sheaves is based on the $K$-theory and Gysin maps of sheaf stacks. In this paper, we generalize the virtual torus localization and cosection localization formulas and their combination to the setting of almost perfect obstruction theory. To this end, we further investigate the $K$-theory of sheaf stacks and its functoriality properties. As applications of the localization formulas, we establish a $K$-theoretic wall crossing formula for simple $\mathbb{C}^\ast$-wall crossings and define $K$-theoretic invariants refining the Jiang-Thomas virtual signed Euler characteristics.
