Complex Tori

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.