Compact Riemann surfaces and Abelian Varieties

  • Günter Harder
Part of the Aspects of Mathematics book series (ASMA, volume 35)


Let S be such a surface. It has a canonical orientation (see section 4.10.2). On pages 77 and 146 we have seen that the cohomology groups of such a surface are given by
$$\begin{array}{*{20}{c}} {{H^\circ }(S, {\cal Z}) = {\cal Z}} \\ {{H^1}(S,{\cal Z}) = {{\cal Z}^{2g}}} \\ {{H^2}(S,{\cal Z}) = {\cal Z}} \\ \end{array}$$


Riemann Surface Line Bundle Meromorphic Function Elliptic Curve Elliptic Curf 
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Copyright information

© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011

Authors and Affiliations

  • Günter Harder
    • 1
  1. 1.Max-Planck-Institute for MathematicsBonnGermany

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