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 language | English |
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Pages (from-to) | 407-418 |
Number of pages | 12 |
Journal | Topology |
Volume | 37 |
Issue number | 2 |
DOIs | |
Publication status | Published - 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.
Funders | Funder number |
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Engineering and Physical Sciences Research Council | GR/J38932 |
University of Liverpool |
ASJC Scopus subject areas
- Geometry and Topology