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A Hitchin–Kobayashi Correspondence for Coherent Systems on Riemann Surfaces
Author(s) -
Bradlow Steven B.,
GarcíaPrada Oscar
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461079900767x
Subject(s) - holomorphic function , mathematics , orthonormality , hermitian matrix , mathematical analysis , pure mathematics , mathematical physics , orthonormal basis , physics , quantum mechanics
A coherent system ( E , V ) consists of a holomorphic bundle plus a linear subspace of its space of holomorphic sections. Motivated by the usual notion in geometric invariant theory, a notion of slope stability can be defined for such objects. In the paper it is shown that stability in this sense is equivalent to the existence of solutions to a certain set of gauge theoretic equations. One of the equations is essentially the vortex equation (that is, the Hermitian–Einstein equation with an additional zeroth order term), and the other is an orthonormality condition on a frame for the subspace V ⊂ H 0 ( E ).