Contributions to Several Complex Variables: In Honour of Wilhelm Stoll (Aspects of Mathematics, Vol E9)

In 1960 Wilhelm Stoll joined the University of Notre Dame faculty as Professor of Mathematics, and in October, 1984 the university acknowledged his many years of distinguished service by holding a conference in complex analysis in his honour. This volume is the proceedings of that conference. It was our priviledge to serve, along with Nancy K. Stanton, as conference organizers. We are grateful to the College of Science of the University of Notre Dame and to the National Science Foundation for their support. In the course of a career that has included the publication of over sixty research articles and the supervision of eighteen doctoral students, Wilhelm Stoll has won the affection and respect of his colleagues for his diligence, integrity and humaneness. The influence of his ideas and insights and the subsequent investigations they have inspired is attested to by several of the articles in the volume. On behalf of the conference partipants and contributors to this volume, we wish Wilhelm Stoll many more years of happy and devoted service to mathematics. Alan Howard Pit-Mann Wong VII III ~ c: ... ~ c: o U CI> .r. ~ .... o e ::J ~ o a:: a. ::J o ... (.!:J VIII '" Q) g> a. '" Q) E z '" ..... o Q) E Q) ..c eX IX Participants on the Group Picture Qi-keng LU, Professor, Chinese Academy of Science, Peking, China. Cover......Page 1 List of Publicatiions of this Series......Page 2 Title: Contributions to Several Complex Variables......Page 3 ISBN 3-528-08964-4......Page 4 Contents......Page 5 Picture of Wilhelm Stoll......Page 6 Foreword......Page 7 Group Picture of the Conference Participants......Page 8 Scheme of the Group Picture......Page 9 Participants on the Group Picture......Page 10 INTRODUCTION......Page 13 0. NOTATION AND PRELIMINARY REMARKS......Page 14 1.1 DEFINITIONS......Page 16 1.2 SPECIAL POINTS OF GIVEN TYPE......Page 17 1.3 ACTION OF THE GALOIS GROUP AND OF G(Af)......Page 18 1.4 OPERATION OF THE IDELES......Page 19 1.5 RATIONAL STRUCTURES. ARITHMETIC MODULAR FUNCTIONS......Page 20 1.6 THE JK-LEVEL CLASS POLYNOMIAL......Page 21 1.7 IK-LEVEL MODULAR CORRESPONDENCES AND THEIR FIXED POINTS......Page 22 2.1 TOPOLOGICAL PROPERTIES OF CORRESPONDENCES AND THE ARTIN KERNEL......Page 24 2.2 FIXED POINTS OF MODULAR CORRESPONDENCES......Page 25 2.3 RATIONALITY OF B over K......Page 27 2.3.1 A LEMMA BASED ON A RESULT OF E. ARTIN [1]......Page 30 3 THE RATIONALITY OF B OVER K......Page 33 3.1 STABILIZER SUBGROUPS AND FIXED POINTS OF CORRESPONDENCES......Page 34 3.2 MULTIPLIER POLYNOMIALS......Page 36 3.3 RATIONALITY OF THE MULTIPLIER POLYNOMIAL......Page 37 3.4 PROOF THAT B IS RATIONAL OVER K......Page 40 4. ABELIAN EXTENSIONS GENERATED BY SPECIAL VALUES......Page 43 REFERENCES......Page 51 1. BACKGROUND......Page 53 2. STRICTLY PSEUDOCONVEX DOMAINS......Page 55 BIBLIOGRAPHY......Page 61 1. INTRODUCTION......Page 63 §1. The Inverse Twister Transform......Page 64 §2. The Geometric Construction......Page 68 §3. Global Calculations......Page 73 §4. Final Remarks......Page 78 REFERENCES......Page 79 1. Introduction......Page 81 2. CUrvature conditions......Page 83 3.The boundary of a::mplete Kahler domains......Page 86 4. Pseudooonvexi ty and weak 1-convexi ty......Page 95 References......Page 97 On the Minimality of Hyperplane Sections of Gorenstein Threefolds......Page 101 §0 NOTATION AND BACKGROUND MATERIAL......Page 102 §1 The Adjunction Process......Page 113 §2 Proof of the Main Theorem......Page 119 References......Page 123 Introduction......Page 127 § 1. The Crucial Lemma......Page 131 § 2. Proof of the Proposition (n)......Page 139 § 3. The Proof of the Main Theorem......Page 145 § 4. Quotients by Lie Groups. Meromorphic Reduction......Page 148 § 5. Appendix......Page 153 Bibliography......Page 159 1. INTRODUCTION......Page 161 2. SOME BASIC METHODS......Page 166 3. THE BASE OF THE 1-ANTICANONICAL FIBRATION OF A COMPACT HOMOGENEOUS CR-HYPERSURFACE......Page 171 4. THE FIBER OF THE1-ANTICANONICAL FIBRATION; CLASSIFICATION AND THE CASE OF NON-DEGENERATE LEVI FORM......Page 178 5. CLASSIFICATION OF K~HLERIAN CR-HYPERSURFACES......Page 183 References......Page 187 INTROOOCTICN......Page 191 I. PLURIPOIJIR SETS AND CCNI'ROL SETS (see [9b] )......Page 193 II. THE GENERAL RESULTS OF L.GRUMAN (see [7] )......Page 197 III. SPEX::IAL PIDPERI'IES OF A MAPPING WI'IH FIBER OF FINITE ORDER.......Page 199 BIBLIOGRAPHY......Page 202 0. Introduction......Page 205 Acknowledgenent.......Page 207 1 . On the proof of Theorem 0. 1......Page 208 2. Estimating the boundary distance......Page 210 3. The relative position of a real analytic hypersurface and a holorrorphic curve......Page 214 4. More on the relative position of a real analytic hypersurface and a holarorphic curve......Page 218 5. Proof of Theorem 0. 1......Page 220 6. Concluding Remarks......Page 224 References......Page 226 1. INTRODUCTION......Page 229 2. CAPACITY OF THE MONGE-AMPERE OPERATOR......Page 230 Construction of the Cantor Sets......Page 232 Construction of the Parameter Functions......Page 233 Basic Inequality for the Mange-Ampere Operator......Page 236 REFERENCES......Page 238 Logarithmic Jet Spaces and Extensions of de Franchis' Theorem......Page 239 §1 LOGARITHMIC JET SP~CES......Page 240 §2 HOLOMORPHIC MAPPINGS INTO SUBVARIETIES OF GENERAL TYPE OF QUASI-ABELIAN VARIETIES......Page 249 §3 RATIONAL MAPPINGS INTO ALGEBRAIC VARIETIES WITH QUASI-NEGATIVE Tq(V; log D)......Page 256 REFERENCES......Page 261 Remarks on the Nakano Vanishing Theorem......Page 263 REFERENCES......Page 271 Curvature of the Weii-Petersson Metric in the Moduli Space of Compact Kihlet-Einstein Manifolds of Negative First Chern Class......Page 273 §1. Canonical Lifting of Vector Fields.......Page 277 §2. Lie Derivatives......Page 279 §3. Kahler Condition.......Page 283 §4. First Part of the Curvature Computation......Page 287 §5. Second Part of the Curvature Computation.......Page 298 REFERENCES......Page 310 INTRODUCTION......Page 311 1) EXTENSION OF ANALYTIC SEI'S AND OF CLOSED POSITIVE CURRENTS......Page 312 2) Pluripositive currents.......Page 321 3) Extension across c. R. sul:manifold......Page 324 4) The canplex Monge-Ampere operator and the extension of meromerphic map......Page 330 5) Extention fran an oem set to C^n......Page 333 6) Open problens......Page 335 B I B L I 0 G R A P H I E......Page 338 Introduction......Page 341 §1 Value Distribution on Parabolic Manifolds......Page 342 §2 Geometry of the Complex Homoqeneous Monge-Amp~re Equation......Page 347 §3 Uniformization Theorems......Page 351 §4 Bounded Monge-Ampere exhaustions......Page 355 §5 Intrinsic metrics in the bounded case......Page 358 Appendix......Page 361 References......Page 363