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