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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
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
- Information
- Proceedings of the London Mathematical Society , Volume 89 , Issue 3 , November 2004 , pp. 570 - 622
- Copyright
- 2004 London Mathematical Society
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