On the Cohomology of Moduli Spaces of Rank Two Vector Bundles Over Curves

  • Don Zagier
Part of the Progress in Mathematics book series (PM, volume 129)


Let C be a Riemann surface, L a line bundle over C, and n a natural number. Then there is a moduli space of stable n-dimensional vector bundles E over C with determinant bundle Λ n (E) ≡ L; this moduli space is smooth but in general non-compact and can be compactified by the suitable addition of semi-stable bundles to a projective, but in general singular, variety N c,n,L .The topology of this variety depends only on the genus g of C and the degree d of L (in fact, only on d modulo n, since tensoring E with a fixed line bundle L 1 replaces L by LL 1 n ), so we will also use the notation N g,n,d . We will be studying only the case n = 2, and hence will drop the n and replace d by ε = (−1)d in the notation. Thus for each g we have two moduli spaces of stable 2-dimensional bundles N g and N g + , both projective varieties of complex dimension 3g − 3. We will be looking mostly at the smooth space N g and will often denote it simply N g .


Modulus Space Vector Bundle Line Bundle Intersection Number Chern Class 
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Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • Don Zagier
    • 1
    • 2
  1. 1.Max-Planck-Institut für MathematikBonnGermany
  2. 2.Universiteit UtrechtThe Netherlands

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