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

Autorentext

Herbert Lange, now retired, was a professor at the department of mathematics of the University Erlangen-Nuremberg. He has published more than 130 research papers on abelian varieties, curve theory and vector bundles on algebraic curves, as well as several books.

Klappentext
This work is at the crossroads of a number of mathematical areas, including algebraic geometry, several complex variables, differential geometry, and representation theory. It is the first book to cover complex tori, among the simplest of complex manifolds, which are important to research in the above areas. The book gives a systematic approach to the theory, presents new results, and includes an up-to-date bibliography.

Inhalt
1 Complex Tori.- 1 Homomorphisms of Complex Tori.- 2 Line Bundles.- 3 The Néron-Severi Group.- 4 The Dual Complex Torus.- 5 Extensions of Complex Tori.- 6 Complementary Subtori and Shafarevich Extensions.- 7 Simple and Indecomposable Complex Tori.- 8 The Endomorphism Algebra of a Complex Torus.- 9 The Theorem of Oort and Zarhin.- 10 The Space of all Complex Tori of Dimension g.- 2 Nondegenerate Complex Tori.- 1 Polarizations of Index k.- 2 Moduli Spaces of Nondegenerate Complex Tori.- 3 The Rosati Involution.- 4 The Dual Polarization.- 5 Poincaré's Reducibility Theorem for Nongenerate Complex Tori.- 6 The Algebraic Dimension.- 7 Picard Number and Algebraic Dimension of Complex Tori of Dimension 2.- 3 Embeddings into Projective Space.- 1 Kähler Theory of Line Bundles on Complex Tori.- 2 Harmonic Forms with Values in a Nondegenerate Line Bundle.- 3 Maps Associated to a Nondegenerate Line Bundle.- 4 The Family of Abelian Varieties Associated to a Nondegenerate Complex Torus.- 5 Some Properties of the Diffeomeorphism ?v: X ? Xv.- 6 The Rational C?-map ?L,V_: X ? ?N.- 4 Intermediate Jacobians.- 1 Primitive Cohomology of Kähler Manifolds.- 2 The Griffiths Intermediate Jacobian.- 3 Some Properties of the Griffiths Intermediate Jacobian.- 4 The Weil Intermediate Jacobian.- 5 The Lazzeri Intermediate Jacobian.- 6 The Abelian Variety Associated to the Griffiths Intermediate Jacobian.- 5 Families of Complex Tori.- 1 Complex Tori with Endomorphism Structure.- 2 The Index of a Complex Torus with Endomorphism Structure.- 3 Complex Tori with Endomorphism Structure of Type Ia.- 4 Complex Tori with Endomorphism Structure of Type Ib.- 5 Complex Tori with Endomorphism Structure of Type II.- 6 The Parameter Spaces of Complex Tori with Endomorphism Structure.- 1 The SpaceHg,k.- 2 The Space Km.- 3 The Space Lm,j.- 4 The Space Mm,k.- 5 The Space Nm,k.- 6 The Space Rm,j.- 7 The Space Sn.- 8 The Space Tn.- 9 The Space U(p,q),j.- 10 The Space Vp,q.- 7 Moduli Spaces.- 1 Moduli Problems.- 2 Homogeneous Spaces with Noncompact Stabilizer.- 3 The Moduli Space of all Complex Tori.- 4 Moduli Spaces of Nondegenerate Complex Tori.- 5 Moduli Spaces of Nondegenerate Complex Tori with Endomorphism Structure.- A The Kronecker Product.- B Anti-Involutions on R-Algebras.- C Complex Structures.- References.- Glossary of Notations.