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

A. D. King, P. E. Newstead

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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
Issue number2
Publication statusPublished - Mar 1998

ASJC Scopus subject areas

  • Geometry and Topology

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