论文标题
关于装饰的半固定G型的自动形态学
On automorphisms of semistable G-bundles with decorations
论文作者
论文摘要
我们证明了某些堆栈点的自动形态的刚性结果，该点承认足够的模量空间。它涵盖了平滑的投影曲线上的$ g $捆绑模量的特殊情况变化，用于还原代数组$ g $。例如，我们的结果适用于可分离的$ g $捆绑包，可分离的Hitchin Pairs堆栈以及一堆可分配的抛物线寄生寄生虫$ G $捆绑包。类似的论点适用于Gieseker在较高维度上的$ G $捆绑包。我们提出了主要结果的两个应用。首先，我们表明，在特征性$ 0 $中，每个可分配装饰的$ g $捆绑包，承认quasiproigntive良好的模量空间可以自然写作为$ g $ linearearized $ y/g $，因此可以将Moduli问题解释为git问题。其次，我们给出证明，在一个特征$ 0 $的任何基础上，曲线家庭上的一堆可半粘的$ g $ -g $ -higgs捆绑均光滑。
We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of $G$-bundles on a smooth projective curve for a reductive algebraic group $G$. For example, our result applies to the stack of semistable $G$-bundles, stacks of semistable Hitchin pairs, and stacks of semistable parabolic $G$-bundles. Similar arguments apply to Gieseker semistable $G$-bundles in higher dimensions. We present two applications of the main result. First, we show that in characteristic $0$ every stack of semistable decorated $G$-bundles admitting a quasiprojective good moduli space can be written naturally as a $G$-linearized global quotient $Y/G$, so the moduli problem can be interpreted as a GIT problem. Secondly, we give a proof that the stack of semistable meromorphic $G$-Higgs bundles on a family of curves is smooth over any base in characteristic $0$.
