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 Λn(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 L ⊗ L n1 ), 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 .
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© 1995 Birkhäuser Boston
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Zagier, D. (1995). On the Cohomology of Moduli Spaces of Rank Two Vector Bundles Over Curves. In: Dijkgraaf, R.H., Faber, C.F., van der Geer, G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4264-2_20
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DOI: https://doi.org/10.1007/978-1-4612-4264-2_20
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8714-8
Online ISBN: 978-1-4612-4264-2
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