Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles

Steven Bradlow; Oscar García-Prada; Peter Gothen; Jochen Heinloth

doi:10.1093/oso/9780198802020.003.0018

Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles

Steven Bradlow, Oscar García-Prada, Peter Gothen, Jochen Heinloth

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We give necessary and sufficient conditions for moduli spaces of semi-stable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL _n -Higgs bundles and the irreducible components of moduli of systems of Hodge bundles on curves. As we do not impose coprimality restrictions, we can apply this to prove connectedness for moduli spaces of U(p, q)-Higgs bundles.

Original language	English (US)
Title of host publication	Geometry and Physics
Subtitle of host publication	A Festschrift in Honour of Nigel Hitchin
Publisher	Oxford University Press
Pages	455-470
Number of pages	16
Volume	2
ISBN (Electronic)	9780198802020
DOIs	https://doi.org/10.1093/oso/9780198802020.003.0018
State	Published - Jan 1 2018

Keywords

Higgs bundle
Hodge bundle
Moduli space
Nilpotent cone
Semi-stable chain

ASJC Scopus subject areas

General Mathematics

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10.1093/oso/9780198802020.003.0018

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AU - Gothen, Peter

AU - Heinloth, Jochen

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N2 - We give necessary and sufficient conditions for moduli spaces of semi-stable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL n -Higgs bundles and the irreducible components of moduli of systems of Hodge bundles on curves. As we do not impose coprimality restrictions, we can apply this to prove connectedness for moduli spaces of U(p, q)-Higgs bundles.

AB - We give necessary and sufficient conditions for moduli spaces of semi-stable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL n -Higgs bundles and the irreducible components of moduli of systems of Hodge bundles on curves. As we do not impose coprimality restrictions, we can apply this to prove connectedness for moduli spaces of U(p, q)-Higgs bundles.

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KW - Nilpotent cone

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Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles

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Keywords

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