# Tagged Questions

**22**

votes

**4**answers

2k views

### What is the precise statement of the correspondence between stable Higgs bundles on a Riemann surface, solutions to Hitchin's self-duality equations on the Riemann surface, and representations of the fundamental group of the Riemann surface?

I am trying to find the precise statement of the correspondence between stable Higgs bundles on a Riemann surface $\Sigma$, (irreducible) solutions to Hitchin's self-duality equations on $\Sigma$, and ...

**2**

votes

**1**answer

404 views

### gauge theory construction of vector bundles on singular varieties

This is sort of a follow-up to:
Gauge theory construction of moduli of vector bundles
If I have a complex compact algebraic curve with at worst nodal singularities, is there an analytic description ...

**6**

votes

**3**answers

1k views

### Gauge theory construction of moduli of vector bundles

Given a smooth projective complex variety $X$, instead of using Mumford's GIT to construct the moduli of rank $n$ topologically trivial vector bundles, we can also take the gauge theory approach.
To ...