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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
Author(s) -
Earl Richard,
Kirwan Frances
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014832
Subject(s) - mathematics , holomorphic function , moduli space , riemann surface , pure mathematics , cohomology , moduli , surface (topology) , mathematical analysis , geometry , physics , quantum mechanics
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. 2000 Mathematics Subject Classification 14H60.