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A HITCHIN–KOBAYASHI CORRESPONDENCE FOR COHERENT SYSTEMS ON RIEMANN SURFACES

Published online by Cambridge University Press:  01 August 1999

STEVEN B. BRADLOW  and
OSCAR GARCÍA-PRADA
STEVEN B. BRADLOW
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA; [email protected]
OSCAR GARCÍA-PRADA
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain; [email protected]
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Abstract

A coherent system ([Escr ], 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⊂H0([Escr ]).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 155 - 170
Copyright
The London Mathematical Society 1999

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