Complex Geometry

by Bauer, Ingrid C.; Catanese, Fabrizio; Kawamata, Yujiro; Peternell, Thomas; Siu, Yum-Tong

• ISBN13: 9783540432593
• ISBN10: 3540432590
• Format: Hardcover
• Copyright: 2002-08-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	v
List of Research Publications of Hans Grauert	vii
List of Doctoral Students of Hans Grauert	xii
Program of Gottingen Conference for the 70th Birthday of Hans Grauert	xiv
List of Participants of Gottingen Conference	xvi
Even Sets of Eight Rational Curves on a K3-surface	1	(26)
Wolf Barth
Introduction	1	(2)
Double Sextics with Eight Nodes	3	(1)
Double Sextics with Eight Tritangents	4	(8)
Quartic Surfaces with Eight Nodes	12	(2)
Quartic Surfaces with Eight Lines	14	(7)
Double Quadrics with Eight Nodes	21	(2)
Double Quadrics with Eight Double Tangents	23	(1)
Comments	24	(3)
References	24	(3)
A Reduction Map for Nef Line Bundles	27	(10)
Thomas Bauer
Frederic Campana
Thomas Eckl
Stefan Kebekus
Thomas Peternell
Stawomir Rams
Tomasz Szemberg
Lorenz Wotzlaw
Introduction	27	(1)
A Reduction Map for Nef Line Bundles	28	(6)
A Counterexample	34	(3)
References	36	(1)
Canonical Rings of Surfaces Whose Canonical System has Base Points	37	(36)
Ingrid C. Bauer
Fabrizio Catanese
Roberto Pignatelli
Introduction	37	(5)
Canonical Systems with Base Points	42	(7)
The Canonical Ring of Surfaces with K2 = 7, pg = 4 Birational to a Sextic: From Algebra to Geometry	49	(9)
The Canonical Ring of Surfaces with K2 = 7, pg = 4 Birational to a Sextic: Explicit Computations	58	(5)
An Explicit Family	63	(10)
References	67	(2)
Appendix 1	69	(1)
Appendix 2	70	(3)
Attractors	73	(12)
Araceli M. Bonifant
John Erik Fornæss
Introduction	73	(1)
Endomorphisms	74	(3)
Hyperbolic Diffeomorphisms	77	(2)
Holomorphic Endomorphisms of Pk	79	(6)
References	83	(2)
A Bound on the Irregularity of Abelian Scrolls in Projective Space	85	(8)
Ciro Ciliberto
Klaus Hulek
Introduction	85	(1)
Non-Existence of Scrolls	86	(2)
Existence of Scrolls	88	(5)
References	92	(1)
On the Frobenius Integrability of Certain Holomorphic p-Forms	93	(6)
Jean-Pierre Demailly
Main Results	93	(2)
Proof of the Main Theorem	95	(4)
References	97	(2)
Analytic Moduli Spaces of Simple (Co)Framed Sheaves	99	(12)
Hubert Flenner
Martin Lubke
Introduction	99	(2)
Preparations	101	(3)
Simple F-Coframed Sheaves	104	(1)
Proof of Theorem 1.1	105	(6)
References	108	(3)
Cycle Spaces of Real Forms of SLn(C)	111	(24)
Alan T. Huckleberry
Joseph A. Wolf
Background	111	(3)
Schubert Slices	114	(7)
Cycle Spaces of Open Orbits of SLn (R) and SLn (H)	121	(14)
References	132	(3)
On a Relative Version of Fujita's Freeness Conjecture	135	(12)
Yujiro Kawamata
Introduction	135	(2)
Review on the Hodge Bundles	137	(1)
Parabolic Structure in Several Variables	138	(3)
Base Change and a Relative Vanishing Theorem	141	(3)
Proof of Theorem 1.7	144	(3)
References	146	(1)
Characterizing the Projective Space after Cho, Miyaoka and Shepherd-Barron	147	(10)
Stefan Kebekus
Introduction	147	(1)
Setup	148	(2)
Proof of the Characterization Theorem	150	(7)
References	154	(3)
Manifolds With Nef Rank 1 Subsheaves in Ω1X	157	(8)
Stefan Kebekus
Thomas Peternell
Andrew J. Sommese
Introduction	157	(1)
Generalities	158	(1)
The Case Where k(X) = 1	158	(1)
The Case Where k(X) = 0	159	(6)
References	163	(2)
The Simple Group of Order 168 and K3 Surfaces	165	(20)
Keiji Oguiso
De-Qi Zhang
Introduction	165	(3)
The Niemeier Lattices	168	(2)
Proof of the Main Theorem	170	(15)
References	180	(5)
A Precise L2 Division Theorem	185	(8)
Takeo Ohsawa
Introduction	185	(1)
L2 Extension Theorem on Complex Manifolds	186	(2)
Extension and Division	188	(1)
Proof of Theorem	189	(4)
References	191	(2)
Irreducible Degenerations of Primary Kodaira Surfaces	193	(40)
Stefan Schroer
Bernd Siebert
Introduction	193	(2)
Smooth Kodaira Surfaces	195	(2)
D-semistable Surfaces with Trivial Canonical Class	197	(2)
Hopf Surfaces	199	(8)
Ruled Surfaces over Elliptic Curves	207	(4)
Rational Surfaces and Honeycomb Degenerations	211	(6)
The Completed Moduli Space and its Boundary	217	(16)
References	221	(12)
Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type	233	(46)
Yum-Tong Siu
Introduction	224	(4)
Review of Existing Argument for Invariance of Plurigenera	228	(6)
Global Generation of Multiplier Ideal Sheaves with Estimates	234	(7)
Extension Theorems of Ohsawa-Takegoshi Type from Usual Basic Estimates with Two Weight Functions	241	(7)
Induction Argument with Estimates	248	(8)
Effective Version of the Process of Taking Powers and Roots of Sections	256	(8)
Remarks on the Approach of Generalized Bergman Kernels	264	(15)
References	276	(3)
Base Spaces of Non-Isotrivial Families of Smooth Minimal Models	279	(50)
Eckart Viehweg
Kang Zuo
Differential Forms on Moduli Stacks	283	(4)
Mild Morphisms	287	(7)
Positivity and Ampleness	294	(7)
Higgs Bundles and the Proof of 1.4	301	(13)
Base Spaces of Families of Smooth Minimal Models	314	(2)
Subschemes of Moduli Stacks of Canonically Polarized Manifolds	316	(5)
A Vanishing Theorem for Sections of Symmetric Powers of Logarithmic One Forms	321	(8)
References	327	(2)
Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians	329
Jaroslaw A. Wisniewski
Introduction	329
M-Uniform Manifolds	331
Atiyah Extension and Twisted Trivial Bundles	333
Characterization of Grassmann Manifolds	336
Characterization of Isotropic Grassmann Manifolds	337
References	339