Abstract
In this chapter we compute the dimension of every cohomology group of every line bundle L on a complex torus X = V/∧ (see Theorem 3.5.5). 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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© 2004 Springer-Verlag Berlin Heidelberg
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Birkenhake, C., Lange, H. (2004). Cohomology of Line Bundles. In: Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften, vol 302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06307-1_5
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DOI: https://doi.org/10.1007/978-3-662-06307-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05807-3
Online ISBN: 978-3-662-06307-1
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