All Questions

$\DeclareMathOperator\SO{SO}\DeclareMathOperator\SL{SL}\DeclareMathOperator\GL{GL}$Let $X$ be a compact Riemann surface. Let $G$ be a real reductive Lie group, $H$ be a maximal compact subgroup of $G$ ...

I'm reading the Bruzzo and Graña Otero's paper Semistable and Numerically Effective Principal (Higgs) Bundles; here: $X$ is a smooth, complex, projective variety; $G$ is a connected, complex, ...

Let $\bar{X}$ be a compact Riemann surface of genus $g$, and let $D:=\{p_{1},p_{2},\cdots,p_{n}\}$ be $n$ distinct points on $\bar{X}$. Define $X:=\bar{X}-D$ to be the punctured Riemann surface given ...

I am reading the book "The Geometry and Dynamics of Magnetic Monopoles", by M.F. Atiyah and N.J. Hitchin, and I got to this part: "... let $H$ be the Hopf line bundle over $S^2$ and ...