nLab
stable bundle
to be merged with stable vector bundle .

Context
Bundles
bundles

Context
Classes of bundles
Universal bundles
Presentations
Examples and Applications
Contents
Idea
A vector bundle over a Riemann surface is called stable (resp. semistable ) if the ratio of its degree and its rank is bigger (resp. bigger or equal) than this ratio for any of its subbundles.

This means that it is a stable point under the action of automorphisms .

Properties
References
Many references are at moduli space of bundles . The notion was introduced by David Mumford in the context of GIT in 1960-s:

D. Mumford, J. Fogarty, F. Kirwan, (1994), Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34 , 3rd ed. Springer 1994

Gerd Faltings , Stable G-bundles and projective connections , J. Alg. Geometry , 2 (1993) pp. 507–568 MR1211997 Zbl 0790.14019

See also

Revised on July 14, 2014 08:00:30
by

Urs Schreiber
(89.204.135.179)