geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
For $\Sigma$ a Riemann surface, a complex vector bundle $E \to \Sigma$ over $\Sigma$ is called stable if for all non-trivial subbundles $K \hookrightarrow E$ the inequality
between the fractions of degree and rank of the vector bundles holds.
The Narasimhan–Seshadri theorem identifies moduli spaces of stable vector bundles with those of certain flat connections.
The notion was introduced in
and
A textbook account is in
See also
Paolo de Bartolomeis, Gang Tian, Stability of complex vector bundles, Journal of Differential Geometry, Vol. 43, No. 2 (1996) (pdf)
Wei-Ping Li, Zhenbo Qin, Stable vector bundles on algebraic surfaces (pdf)