Complex Geometry

Even Sets of Eight Rational Curves on a K3-surface.- 0 Introduction.- 1 Double Sextics with Eight Nodes.- 2 Double Sextics with Eight Tritangents.- 3 Quartic Surfaces with Eight Nodes.- 4 Quartic Surfaces with Eight Lines.- 5 Double Quadrics with Eight Nodes.- 6 Double Quadrics with Eight Double Tangents.- 7 Comments.- References.- A Reduction Map for Nef Line Bundles.- 1 Introduction.- 2 A Reduction Map for Nef Line Bundles.- 3 A Counterexample.- References.- Canonical Rings of Surfaces Whose Canonical System has Base Points.- 0 Introduction.- 1 Canonical Systems with Base Points.- 2 The Canonical Ring of Surfaces with K2 = 7, pg = 4 Birational to a Sextic: From Algebra to Geometry.- 3 The Canonical Ring of Surfaces with K2 = 7, pg = 4 Birational to a Sextic: Explicit Computations.- 4 An Explicit Family.- References.- Appendix 1.- Appendix 2.- Attractors.- 1 Introduction.- 2 Endomorphisms.- 3 Hyperbolic Diffeomorphisms.- 4 Holomorphic Endomorphisms of ?k.- References.- A Bound on the Irregularity of Abelian Scrolls in Projective Space.- 0 Introduction.- 1 Non-Existence of Scrolls.- 2 Existence of Scrolls.- References.- On the Frobenius Integrability of Certain Holomorphic p-Forms.- 1 Main Results.- 2 Proof of the Main Theorem.- References.- Analytic Moduli Spaces of Simple (Co)Framed Sheaves.- 1 Introduction.- 2 Preparations.- 3 Simple F-Coframed Sheaves.- 4 Proof of Theorem 1.1.- References.- Cycle Spaces of Real Forms of SLn(?).- 1 Background.- 2 Schubert Slices.- 3 Cycle Spaces of Open Orbits of SLn(?) and SLn(?).- References.- On a Relative Version of Fujita's Freeness Conjecture.- 1 Introduction.- 2 Review on the Hodge Bundles.- 3 Parabolic Structure in Several Variables.- 4 Base Change and a Relative Vanishing Theorem.- 5 Proof of Theorem 1.7.-References.- Characterizing the Projective Space after Cho, Miyaoka and Shepherd-Barron.- 1 Introduction.- 2 Setup.- 3 Proof of the Characterization Theorem.- References.- Manifolds With Nef Rank 1 Subsheaves in $$ \Omega_X^1 $$.- 1 Introduction.- 2 Generalities.- 3 The Case Where ?(X) = 1.- 4 The Case Where ?(X) = 0.- References.- The Simple Group of Order 168 and K3 Surfaces.- 0 Introduction.- 1 The Niemeier Lattices.- 2 Proof of the Main Theorem.- References.- A Precise L2 Division Theorem.- 0 Introduction.- 1 L2 Extension Theorem on Complex Manifolds.- 2 Extension and Division.- 3 Proof of Theorem.- References.- Irreducible Degenerations of Primary Kodaira Surfaces.- 0 Introduction.- 1 Smooth Kodaira Surfaces.- 2 D-semistable Surfaces with Trivial Canonical Class.- 3 Hopf Surfaces.- 4 Ruled Surfaces over Elliptic Curves.- 5 Rational Surfaces and Honeycomb Degenerations.- 6 The Completed Moduli Space and its Boundary.- References.- Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type.- 0 Introduction.- 1 Review of Existing Argument for Invariance of Plurigenera.- 2 Global Generation of Multiplier Ideal Sheaves with Estimates.- 3 Extension Theorems of Ohsawa-Takegoshi Type from Usual Basic Estimates with Two Weight Functions.- 4 Induction Argument with Estimates.- 5 Effective Version of the Process of Taking Powers and Roots of Sections.- 6 Remarks on the Approach of Generalized Bergman Kernels.- References.- Base Spaces of Non-Isotrivial Families of Smooth Minimal Models.- 1 Differential Forms on Moduli Stacks.- 2 Mild Morphisms.- 3 Positivity and Ampleness.- 4 Higgs Bundles and the Proof of 1.4.- 5 Base Spaces of Families of Smooth MinimalModels.- 6 Subschemes of Moduli Stacks of Canonically Polarized Manifolds.- 7 A Vanishing Theorem for Sections of Symmetric Powers of Logarithmic One Forms.- References.- Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians.- 0 Introduction.- 1 M-Uniform Manifolds.- 2 Atiyah Extension and Twisted Trivial Bundles.- 3 Characterization of Grassmann Manifolds.- 4 Characterization of Isotropic Grassmann Manifolds.- References.