Cover 1
Half-title 3
Title 5
Copyright 6
Dedication 7
Foreword 9
List of Contributors 11
Contents 13
Introduction 15
References 20
Part I 23
Coverings of the Rational Double Points in Characteristic p 25
1. Generalities on Coverings 25
2. Reduction modulo p 28
3. List of the Singularities and their Equations 29
4. The Computations in Characteristic 2 31
5. The Computations in Characteristics 3 and 5 34
References 36
Enriques' Classification of Surfaces in Char, p, II 37
Introduction and Preliminary Reductions 37
List of Notations 40
1. Kx of Elliptic or Quasi-elliptic Surfaces 41
2. Proof of Theorem 1 45
3. Analysis of Hyperelliptic Surfaces 47
4. Proof of Theorem 5 52
5. Analysis of the Case Leading to Abelian Surfaces 53
References 56
Classification of Hilbert Modular Surfaces 57
I. Introduction and Statement of Results 57
II. Numerical Invariants of Hilbert Modular Surfaces 60
III. The Hurwitz-Maa脽 Extension of the Hilbert Modular Group, Skew-Hermitian Curves on Y(D) 68
IV. Estimates of the Numerical Invariants 77
V. The Rough Classification of Hilbert Modular Surfaces 83
References 91
On Algebraic Surfaces with Pencils of Curves of Genus 2 93
Introduction 93
1. A Fundamental Construction 94
2. Elementary Transformations 96
3. Canonical Resolution 98
4. Return to the Original Surface 101
5. A Remark on Base Points 103
References 104
New Surfaces with No Meromorphic Functions, II 105
0. Introduction 105
1. Algebraic Preliminaries 105
2. Construction I 109
3. Construction II 112
4. Topological Properties 114
5. Analytical Properties 117
6. Special Cases with [U(蠅) : U+(蠅)] = 2 118
7. Remarks and Acknowledgements 119
References 120
On the Deformation Types of Regular Elliptic Surfaces 121
References 124
On Numerical Campedelli Surfaces 127
1. Statement of Main Results 127
2. Preliminaries 128
3. Proof of Theorem A 128
4. The Structure of Campedelli Surfaces 130
References 132
On Singular K3 Surfaces 133
1. Elliptic Pencils on a K3 Surface 134
2. Construction of a Certain Elliptic Pencil on a Kummer Surface 135
3. Certain Double Coverings of Kummer Surfaces 138
4. Classification of Singular K3 Surfaces 142
5. Automorphisms 144
6. An Arithmetic Application 147
References 149
On the Minimality of Certain Hilbert Modular Surfaces 151
1. Introduction 151
2. Preliminaries 152
3. The Main Result 156
4. Some Comments 162
References 164
Part II 165
Complex Structures on S2p+l x S2q+l with Algebraic Codimension 1 167
0. Introduction 167
1. Existence Theorem for a Holomorphic Torus Action 168
2. The Construction of Calabi-Eckmann Manifolds 173
3. Complex Structures on S2p+1 x S2q+1 173
References 177
Defining Equations for Certain Types of Polarized Varieties 179
Introduction 179
1. One-dimensional Case 179
2. Climbing a Ladder 182
3. Existence of a Ladder 184
4. Main Theorem in Higher Dimensional Cases 185
5. Applications 186
References 187
On Logarithmic Kodaira Dimension of Algebraic Varieties 189
1. Introduction and Notation 189
2. Examples 190
3 191
4 194
5 196
6 198
7 200
8 202
References 203
On a Characterization of Submanifolds of Hopf Manifolds 205
0. Introduction 205
1. Definitions and Statement of Main Theorem 206
2. Stein Completions and Extensions of Holomorphic Maps 207
3. Subvarieties of Hopf Manifolds 209
4. Proof of Main Theorem 211
References 220
Relative Compactification of the N茅ron Model and its Application 221
Introduction 221
Notation 222
1. Preliminaries 222
2. Existence of a Quotient 224
3. The Neron Model and a Proof of Minimality 226
4. A Family of Curves of Genus Two 229
5. The Case B (p>0) 231
6. The Case B (p, q>0) 234
7. The Case B (p, q, r>0) 236
8. Final Remarks 238
References 239
Toroidal Degeneration of Abelian Varieties 241
1. Torus Embeddings 242
2. Period Map and Degeneration Data 244
3. Construction of Degenerating Fibres 246
4. Applications 249
References 250
Kodaira Dimensions of Complements of Divisors 253
Notations 253
1. Kodaira Dimensions of Non-Compact Complex Manifolds 254
2. Complements of Divisors 257
3. Bergman Kernel Forms 261
4. Extension of Holomorphic Maps 264
5. Representation of the Group of Bimeromorphic Transformations 266
Appendix 268
References 270
Compact Quotients of C3 by Affine Transformation Groups, II 273
1. Closed Holomorphic 1-Forms on C3/N 273
2. Structures 277
3. Holomorphic Forms 288
References 292
Kodaira Dimensions for Certain Fibre Spaces 293
Notations 294
1. Families of Jacobian Varieties 294
2. Conjecture C2 299
3. Fibre Space over a Curve 301
Appendix 304
References 306
Part III 307
Some Remarks on Formal Poincar茅 Lemma 309
1. Preliminaries 309
2. Honest Differential Operators 310
3. The Symbolic Complex 314
References 319
Special Arithmetic Groups and Eisenstein Series 321
Examples 330
References 330
Submanifolds and Over-determined Differential Operators 333
Introduction 333
1. The Linear Differential Operator D 334
2. Submanifolds and Linear Complexes 340
3. The Non-linear Operator D 348
4. Pseudo-complex Structures; Formulas of Kuranishi 359
5. Pseudo-complex Structures and the Non-linear Complex 367
References 370
On the First Terms of Certain Asymptotic Expansions 371
Introduction 371
1. Characteristic Exponents 372
2. A Geometric Theorem 373
3. Algebraic Preliminaries 375
4. Proof of the Theorem 377
5. Asymptotic Formulas 380
References 382
Micro-Local Calculus of Simple Microfunctions 383
1. Micro-Differential Operators 383
2. Symbol of Simple Microfunctions 385
References 388
A Note on Steenrod Reduced Powers of Algebraic Cocycles 389
1. Blowing up of an Algebraic Cocycle 389
2. Proof of Theorem 393
References 395
Polynomial Growth C鈭?de Rham Cohomology and Normalized Series of Prestratified Spaces 397
0. Introduction 397
1. P. g. Simple Prestratificatian 398
1.1. Simple Prestratification 398
1. 2. C鈭?de Rham C.C.I. 399
1.3. P. g. Adequate Prestratified Space and p. g. Simple Prestratification 400
1. 4. P. g. C鈭?de Rham C. C. I. 402
2. P. g. Simple Prestratification and Normalized Series 404
2. 1. Minimal Vertical Refinement of a Normalized Series 405
2. 2. Basic Properties of the Minimal Vertical Refinement 407
2. 2.1. Neighborhoods and certain sets attached to strata in 407
2. 2. 2. P. g. simple C掳掳-thickenings of the minimal vertical refinement 408
2.2.3. P. g. simple property of the minimal vertical refinement 409
References 409
Index 411