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

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

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationGeometry and Physics
Subtitle of host publicationA Festschrift in Honour of Nigel Hitchin
PublisherOxford University Press
Pages455-470
Number of pages16
Volume2
ISBN (Electronic)9780198802020
DOIs
StatePublished - Jan 1 2018

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bradlow, S., García-Prada, O., Gothen, P., & Heinloth, J. (2018). Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles. In Geometry and Physics: A Festschrift in Honour of Nigel Hitchin (Vol. 2, pp. 455-470). Oxford University Press. https://doi.org/10.1093/oso/9780198802020.003.0018