Grassmannian framed bundles and generalized parabolic structures

TL;DR

This paper constructs compact moduli spaces of Grassmannian framed bundles over Riemann surfaces, establishing a Hitchin-Kobayashi correspondence between algebraic and symplectic frameworks, and relates these to parabolic bundles.

Contribution

It introduces a novel construction of moduli spaces using bi-invariant compactifications and extends the Hitchin-Kobayashi correspondence to these spaces and generalized parabolic bundles.

Findings

Established a Hitchin-Kobayashi correspondence for Grassmannian framed bundles.

Constructed universal moduli spaces for parabolic bundles.

Connected algebraic and symplectic moduli space frameworks.

Abstract

We build compact moduli spaces of Grassmannian framed bundles over a Riemann surface, essentially replacing a group by its bi-invariant compactification. We do this both in the algebraic and symplectic settings, and prove a Hitchin-Kobayashi correspondence between the two. The spaces are universal spaces for parabolic bundles, and the reduction to parabolic bundles commutes with the correspondence. An analogous correspondence is outlined for the generalized parabolic bundles of Bhosle.