Abstract
In this chapter we compute the dimension of every cohomology group of every line bundle L on a complex torus X = V/Λ (see Theorem 5.5). As a direct consequence we get a formula for the Euler-Poincaré characteristic χ(L) of L. The result is the Riemann-Roch Theorem. This approach to Riemann-Roch was first given in Deligne [1] and independently in Umemura [1].
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© 1992 Springer-Verlag Berlin Heidelberg
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Lange, H., Birkenhake, C. (1992). Cohomology of Line Bundles. In: Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften, vol 302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02788-2_5
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DOI: https://doi.org/10.1007/978-3-662-02788-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02790-5
Online ISBN: 978-3-662-02788-2
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