Abstract
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 ℱ, G are reserved for locally free O-sheaves. The letter L is usual exclusively for locally free sheaves of rank 1. All tensor products are formed over O.
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© 2004 Springer-Verlag Berlin Heidelberg
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Grauert, H., Remmert, R. (2004). Compact Riemann Surfaces. In: Theory of Stein Spaces. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18921-0_9
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DOI: https://doi.org/10.1007/978-3-642-18921-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00373-1
Online ISBN: 978-3-642-18921-0
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