On automorphisms of semistable G-bundles with decorations
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Andres Fernandez Herrero
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.
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Communicated by: I. Coskun
Acknowledgements
I would like to thank Mark Andrea de Cataldo, Tomás L. Gómez, Daniel Halpern-Leistner and Nicolas Templier for helpful discussions. I would also like to thank anonymous referees for useful comments on the manuscript.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Topology of tropical moduli spaces of weighted stable curves in higher genus
- Explicit p-harmonic functions on the real Grassmannians
- Cohomogeneity one central Kähler metrics in dimension four
- Tropical Poincaré duality spaces
- Isometries of wall-connected twin buildings
- On automorphisms of semistable G-bundles with decorations
- Abelian branched covers of rational surfaces
- Polyhedral compactifications, I
Artikel in diesem Heft
- Frontmatter
- Topology of tropical moduli spaces of weighted stable curves in higher genus
- Explicit p-harmonic functions on the real Grassmannians
- Cohomogeneity one central Kähler metrics in dimension four
- Tropical Poincaré duality spaces
- Isometries of wall-connected twin buildings
- On automorphisms of semistable G-bundles with decorations
- Abelian branched covers of rational surfaces
- Polyhedral compactifications, I
