On automorphisms of semistable G-bundles with decorations

IF 0.5 4区 数学 Q3 MATHEMATICS
Andres Fernandez Herrero
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引用次数: 0

Abstract

Abstract 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, to stacks of semistable Hitchin pairs, and to 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.
带修饰的半稳定g束的自同构
摘要我们证明了一个关于某些点的自同构的刚性结果。作为特例,它包含了一个归约代数群G的光滑投影曲线上G-丛的模的变化。例如,我们的结果适用于半稳定G-丛的堆栈、半稳定Hitchin对的堆栈和半稳定抛物G-丛的堆叠。类似的论点适用于高维的Gieseker半稳定G-丛。我们给出了主要结果的两个应用。首先,我们证明了在特征0中,每一个半稳定修饰G-丛的栈都可以自然地写成G-线性化的全局商Y/G,因此模问题可以解释为GIT问题。其次,我们给出了一个证明,证明了曲线族上的半稳定亚纯G-Higgs丛在特征为0的任何基上是光滑的。
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来源期刊
Advances in Geometry
Advances in Geometry 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
31
审稿时长
>12 weeks
期刊介绍: Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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