Quiver bundles and wall crossing for chains

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Gothen, PB (Author) FCUP; Nozad, A (Author) Other

Journal

Title: Geometriae Dedicata

Vol. 199

Pages: 137-146

ISSN: 0046-5755

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00N-QS9

DOI: 10.1007/s10711-018-0341-6

Abstract (EN): Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin-Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a new proof of a key lemma on chains (due to alvarez-Consul-Garcia-Prada-Schmitt), which has been important in the study of Higgs bundle moduli; this proof relies on stability and thus avoids the direct use of the chain vortex equations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10