Compact Riemann Surfaces

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 236)


In the theory of compact Riemann surfaces it is possible to make particularly elegant applications of the finiteness theorem. For such considerations we will always let X denote a connected, compact Riemann surface with structure sheaf O. With script letters like S we will denote, as before, coherent analytic sheaves over X. If the support of such a sheaf is finite then T will usually be written. For such a sheaf it is easy to see that H 1(X, T) = (0). The symbols , G are reserved for locally free O-sheaves. The letter is usual exclusively for locally free sheaves of rank 1. All tensor products are formed over O.


Exact Sequence Duality Theorem Compact Riemann Surface Divisor Class Free Sheaf 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany
  2. 2.Mathematisches InstitutWestfälischen Wilhelms-UniversitätMünsterFederal Republic of Germany

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