Pseudo-real principal G-bundles over a real curve

2015/02/02 by Indranil Biswas, Biswas, Indranil, Oscar Garcı́a-Prada +3
Mathematics · #14P99 #32Q15 #53C07 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1502.00563

openalex publication_date 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixing suitable topological invariants, one can build a suitable gauge theory, and show that the resulting moduli spaces of pseudo-real bundles are connected. This in turn allows one to describe the various fixed point varieties on the complex moduli spaces under the action of the real involutions on the curve and the structure group.

Related

• Principal bundles over a real algebraic curve
• Strongly Semistable Bundles on a Curve over a finite field
• The structure of the moduli of gauged maps from a smooth curve
• On the moduli space of singular principal G-bundles over stable curves
• Singular principal bundles on reducible nodal curves