stable vector bundle
Classes of bundles
Examples and Applications
For a Riemann surface, a complex vector bundle over is called stable if for all non-trivial subbundles 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
- D. Mumford, Geometric invariant theory, Ergebnisse Math. Vol 34 Springer (1965)
- F. Takemoto, Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47 (1973) and 52 (1973) (Euclid)
A textbook account is in
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)
Revised on November 7, 2012 19:49:04
by Urs Schreiber