论文标题
atiyah班
The equivariant Atiyah class
论文作者
论文摘要
让$ x $成为一个复杂的计划，由仿射代数组$ g $采用。我们证明，正如Huybrechts和Thomas建造的$ g $ Equivariant Perfect Complect的Atiyah类是$ g $ equivariant，从精确的意义上讲是$ g $ equivariant。作为一个应用程序，我们表明，如果$ g $是还原性的，那么在$ g $ invariant的$ g $ invariant Smooth Projective Family $ y \ y to b $的精细相对模量空间$ m \ to b $上的障碍理论是$ g $ equivariant。此处包含的结果旨在建议如何在各种具有圆环动作的模量空间上检查天然阻塞理论的均衡，例如在唐纳森（Donaldson） - 托马斯（Thomas）理论和瓦法理论（Vafa）中引起的。
Let $X$ be a complex scheme acted on by an affine algebraic group $G$. We prove that the Atiyah class of a $G$-equivariant perfect complex on $X$, as constructed by Huybrechts and Thomas, is $G$-equivariant in a precise sense. As an application, we show that, if $G$ is reductive, the obstruction theory on the fine relative moduli space $M\to B$ of simple perfect complexes on a $G$-invariant smooth projective family $Y\to B$ is $G$-equivariant. The results contained here are meant to suggest how to check the equivariance of the natural obstruction theories on a wide variety of moduli spaces equipped with a torus action, arising for instance in Donaldson--Thomas theory and Vafa--Witten theory.
