The moduli space of stable vector bundles over a real algebraic curve

2009/01/20 by Indranil Biswas, Biswas, Indranil, Johannes Huisman +4 · 3 citations
Mathematics · #14D20 (Primary) #14P20 #55R35 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14D20 #msc:14P20 #msc:55R35

paper · pdf · doi:10.48550/arxiv.0901.3071

28 pages; revised version; minor corrections

openalex publication_date 2009/01/20 · arxiv created 2009/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.

Citations

• Vector Bundles Over an Elliptic Curve

Cited by

• Real Bialynicki-Birula flows in moduli spaces of Higgs bundles
• Moduli spaces of twisted equivariant G-bundles over a curve
• Real points of coarse moduli schemes of vector bundles on a real algebraic curve

Related

• Local structure of the moduli space of vector bundles over curves
• Universal vector bundle over the reals
• Birational Models of the Moduli Spaces of Stable Vector Bundles over Curves
• Automorphisms of moduli spaces of vector bundles over a curve
• Rational curves and lines on the moduli space of stable bundles