Titlebook: Complex Abelian Varieties; Christina Birkenhake,Herbert Lange Book 2004Latest edition Springer-Verlag Berlin Heidelberg 2004 Abelian varie

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Haruki Odagiri,Stéphane Guillo,Thomas Bauere are essentially two methods to employ a group . of automorphisms in order to decompose an abelian variety .: If . is cyclic, one can use the set of fixed points of ., and for an arbitrary group . the rational representation algebra ℚ[.], for decomposing . up to isogeny.

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Introduction, different constants ... If . = deg . is 1 or 2, an explicit integration by elementary functions is well known from calculus. If . = 3 or 4, integration is possible using elliptic functions. If however . ≥ 5, no explicit integration is known in general.

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Complex Tori, = ℂ./∧ with . a lattice in ℂ.. The complex torus . is a complex manifold of dimension .. It inherits the structure of a complex Lie group from the vector space ℂ.. A meromorphic function on ℂ., periodic with respect to ., may be considered as a function on .. An. is a complex torus admitting suffic

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Line Bundles on Complex Tori,s that .(.) is an extension of the Néron-Severi group .(.) by the group .(Λ, ℂ.) of characters of Λ with values in the circle group ℂ.. The group .(.) turns out to be the group of hermitian forms . on . satisfying Im . (., .) ⊆ ℤ. The theorem was proven for dimension 2 by Humbert [1] applying a resu

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