arXiv 2202.133602022-02math.AG

On automorphisms of semistable G-bundles with decorations

Andres Fernandez Herrero

备注：: 15 pages. Final accepted version. Comments welcome!

英文摘要：

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 $0$.

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