Overview

This book is a collection of research articles in algebraic geometry and complex analysis dedicated to Hans Grauert. The authors and editors have made their best efforts in order that these contributions should be adequate to honour the outstanding scientist. The volume contains important new results, solutions to longstanding conjectures, elegant new proofs and new perspectives for future research. The topics range from surface theory and commutative algebra, linear systems, moduli spaces, classification theory, Kahler geometry to holomorphic dynamical systems.

Full Product Details

Author:   Ingrid Bauer ,  F. Catanese ,  Y. Kawamata ,  Thomas Peternell
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.530kg
ISBN:  

9783540432593

ISBN 10:   3540432590
Pages:   340
Publication Date:   28 May 2002
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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 Minimal Models.- 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.

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