On the cohomology ring of the moduli space of rank 2 vector bundles on a curve

A. D. King, P. E. Newstead

Research output: Contribution to journalArticlepeer-review

28 Citations (SciVal)

Abstract

Let script Ng be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree over a smooth complex projective curve of genus g. This paper gives a complete and very simple description of the rational cohomology ring H*(script Ng). A structural formula is proved for H*(script Ng), which was originally conjectured by Mumford. It is shown that the first relation in genus g between the standard generators satisfies a recurrence relation, first found by Zagier, and that the invariant subring for the mapping class group is a complete intersection ring. A Gröbner basis is found for the ideal of invariant relations; this leads to a natural monomial basis for H*(script Ng).

Original languageEnglish
Pages (from-to)407-418
Number of pages12
JournalTopology
Volume37
Issue number2
DOIs
Publication statusPublished - Mar 1998

Funding

‘When this research was being done, the first author was at the University of Liverpool supported by the SERC/EPSRC (grant GR/J38932). Both authors are members of the VBAC group of Europroj.

FundersFunder number
Engineering and Physical Sciences Research CouncilGR/J38932
University of Liverpool

ASJC Scopus subject areas

  • Geometry and Topology

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