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

Richard Earl; Frances Kirwan

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arXiv · math/0305345

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

Richard Earl·Frances Kirwan

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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.

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BibTeX RIS

Richard Earl, Frances Kirwan. 2003-05-24. Complete sets of relations in the cohomology rings of moduli spaces of holomorphic bundles and parabolic bundles over a Riemann surface. https://arxiv.org/abs/math/0305345

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