Ebook: Complex Geometry: Collection of Papers Dedicated to Hans Grauert

This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il­ lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car­ tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves.

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Content:
Front Matter....Pages I-XXII
Even Sets of Eight Rational Curves on a K3-surface....Pages 1-25
A Reduction Map for Nef Line Bundles....Pages 27-36
Canonical Rings of Surfaces Whose Canonical System has Base Points....Pages 37-72
Attractors....Pages 73-84
A Bound on the Irregularity of Abelian Scrolls in Projective Space....Pages 85-92
On the Frobenius Integrability of Certain Holomorphic p-Forms....Pages 93-98
Analytic Moduli Spaces of Simple (Co)Framed Sheaves....Pages 99-109
Cycle Spaces of Real Forms of SLn(?)....Pages 111-133
On a Relative Version of Fujita’s Freeness Conjecture....Pages 135-146
Characterizing the Projective Space after Cho, Miyaoka and Shepherd-Barron....Pages 147-155
Manifolds with Nef Rank 1 Subsheaves in ? X 1 ....Pages 157-164
The Simple Group of Order 168 and K3 Surfaces....Pages 165-184
A Precise L 2 Division Theorem....Pages 185-191
Irreducible Degenerations of Primary Kodaira Surfaces....Pages 193-222
Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type....Pages 223-277
Base Spaces of Non-Isotrivial Families of Smooth Minimal Models....Pages 279-328
Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians....Pages 329-340

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Content:
Front Matter....Pages I-XXII
Even Sets of Eight Rational Curves on a K3-surface....Pages 1-25
A Reduction Map for Nef Line Bundles....Pages 27-36
Canonical Rings of Surfaces Whose Canonical System has Base Points....Pages 37-72
Attractors....Pages 73-84
A Bound on the Irregularity of Abelian Scrolls in Projective Space....Pages 85-92
On the Frobenius Integrability of Certain Holomorphic p-Forms....Pages 93-98
Analytic Moduli Spaces of Simple (Co)Framed Sheaves....Pages 99-109
Cycle Spaces of Real Forms of SLn(?)....Pages 111-133
On a Relative Version of Fujita’s Freeness Conjecture....Pages 135-146
Characterizing the Projective Space after Cho, Miyaoka and Shepherd-Barron....Pages 147-155
Manifolds with Nef Rank 1 Subsheaves in ? X 1 ....Pages 157-164
The Simple Group of Order 168 and K3 Surfaces....Pages 165-184
A Precise L 2 Division Theorem....Pages 185-191
Irreducible Degenerations of Primary Kodaira Surfaces....Pages 193-222
Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type....Pages 223-277
Base Spaces of Non-Isotrivial Families of Smooth Minimal Models....Pages 279-328
Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians....Pages 329-340
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