论文标题
唐纳森 - 托马斯捆的双曲线定位
Hyperbolic localization of the Donaldson-Thomas sheaf
论文作者
论文摘要
在本文中，我们证明了共同体唐纳森·托马斯理论中的复曲面定位公式。考虑一个带有-1换速的代数空间，具有C*动作，使-1偏移的符号形式不变。这包括稳定的滑轮的模量空间或带有c*invariant calabi-yau形式的卡拉比（Calabi-Yau）上的束带的束带，或在同一空间中与C*-Invariant simplectic形式的两个C*-Invariant Lagrangians的相交。在这种情况下，我们表达了乔伊斯等人定义的唐纳森 - 托马斯 - thomas变形捆（或单粒子混合霍奇模块）。作为C*固定组件上的DT变形带轮的共同体变化，吸引的品种作为总和。该结果可将其视为平滑方案的bilynicki-birula分解的-1偏移版本。
In this paper we prove a toric localization formula in cohomological Donaldson Thomas theory. Consider a -1-shifted symplectic algebraic space with a C* action leaving the -1-shifted symplectic form invariant. This includes the moduli space of stable sheaves or complexes of sheaves on a Calabi-Yau threefold with a C*-invariant Calabi-Yau form, or the intersection of two C*-invariant Lagrangians in a symplectic space with a C*-invariant symplectic form. In this case we express the restriction of the Donaldson-Thomas perverse sheaf (or monodromic mixed Hodge module) defined by Joyce et al. to the attracting variety as a sum of cohomological shifts of the DT perverse sheaves on the C* fixed components. This result can be seen as a -1-shifted version of the Bialynicki-Birula decomposition for smooth schemes.
