Titlebook: Complex Tori; Christina Birkenhake,Herbert Lange Book 1999 Springer Science+Business Media New York 1999 Abelian variety.Algebra.Cohomolog

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Embeddings into Projective Space,the Riemann-Roch Theorem of [CAV], Chapter 3. It goes back to a trick of Wirtinger [Wi]: A suitable change of the complex structure of . defines in a canonical way a line bundle . which is positive definite and satisfies .(.) = .(.). As we learned from R. R. Simha, this approach appears already in t

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Families of Complex Tori,an anti-involution ’ on End.(.). The skew fields . of finite type over ℚ with anti-involution ′ were classified by Albert. In this chapter we work out which of these algebras can be realized as endomorphism algebras of nondegenerate complex tori.

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Book 1999A complex torus is a connected compact complex Lie group. Any complex 9 9 torus is of the form X =

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Complex Tori,. = ℂ./ Λ with Λ a lattice in ℂ.. A complex torus is a complex manifold of dimension .. It inherits the structure of a complex Lie group from the vector space ℂ.. In this chapter we study some properties of complex tori without any additional structure.

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Intermediate Jacobians, give their definitions, deduce some of their properties and see how they are related. We omit some of their most important aspects, for example the Abel-Jacobi map, which reflects the geometry of the manifold ., since here we are more interested in the complex tori.

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