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Reduction and Extension

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1759)

Abstract

ABE showed that the question of the existence of non—trivial sections in line bundles can be reduced to positive line bundles. With a general concept of a Riemann form he gave a new proof of the existence of the meromorphic reduction of a toroidal group. Recently Takayama proved the conjecture that positive line bundles L always have non—trivial sections. He proved also that Lℓ is very ample for any integer ℓ ≥ 3. For some questions it is useful to extend holomorphic line bundles from a toroidal group to standard compactifications. M. STEIN showed that this is possible, if and only if the Hermitian form defined by the bundle fulfils a certain condition. Abe condersidered the case where the fibration is associated with an ample Riemann form of kind ℓ.

Keywords

Line Bundle Holomorphic Function Meromorphic Function Abelian Variety Automorphic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

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