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Complete sets of relations in the cohomology rings of moduli spaces of holomorphic bundles and parabolic bundles over a Riemann surface

Published online by Cambridge University Press:  05 November 2004

Richard Earl
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford, OX1 3LB, United Kingdom. E-mail: [email protected]
Frances Kirwan
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford, OX1 3LB, United Kingdom. E-mail: [email protected]
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Abstract

The cohomology ring of the moduli space of stable holomorphic vector bundles of rank $n$ and degree $d$ over a Riemann surface of genus $g > 1$ has a standard set of generators when $n$ and $d$ are coprime. When $n = 2$ the relations between these generators are well understood, and in particular a conjecture of Mumford, that a certain set of relations is a complete set, is known to be true. In this article generalisations are given of Mumford's relations to the cases when $n > 2$ and also when the bundles are parabolic bundles, and these are shown to form complete sets of relations.

Type
Research Article
Copyright
2004 London Mathematical Society

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