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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)

Abstract

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 .

Keywords

Modulus Space Vector Bundle Line Bundle Intersection Number Chern Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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