## Singularities: The Brieskorn Anniversary VolumeEgbert Brieskorn, Vladimir Igorevich Arnolʹd, Gert-Martin Greuel, J. H. M. Steenbrink In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests. |

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### Contents

V | 3 |

VI | 4 |

VII | 6 |

VIII | 17 |

IX | 26 |

X | 27 |

XI | 29 |

XII | 32 |

LXXIV | 214 |

LXXV | 222 |

LXXVI | 226 |

LXXVII | 233 |

LXXVIII | 235 |

LXXIX | 237 |

LXXX | 239 |

LXXXI | 241 |

XIII | 36 |

XIV | 37 |

XV | 38 |

XVI | 48 |

XVII | 59 |

XVIII | 61 |

XIX | 63 |

XX | 67 |

XXI | 70 |

XXII | 73 |

XXIII | 78 |

XXIV | 87 |

XXV | 92 |

XXVI | 93 |

XXVII | 94 |

XXVIII | 96 |

XXIX | 98 |

XXX | 100 |

XXXI | 101 |

XXXII | 103 |

XXXIII | 104 |

XXXIV | 108 |

XXXV | 111 |

XXXVI | 114 |

XXXVII | 117 |

XXXVIII | 119 |

XXXIX | 120 |

XL | 123 |

XLI | 126 |

XLII | 127 |

XLIII | 129 |

XLIV | 134 |

XLV | 135 |

XLVI | 138 |

XLVII | 141 |

XLVIII | 142 |

XLIX | 143 |

L | 145 |

LI | 146 |

LII | 150 |

LIII | 152 |

LIV | 155 |

LV | 158 |

LVI | 159 |

LVII | 165 |

LVIII | 167 |

LIX | 170 |

LX | 174 |

LXI | 179 |

LXII | 182 |

LXIII | 187 |

LXIV | 192 |

LXV | 195 |

LXVI | 198 |

LXVII | 199 |

LXVIII | 202 |

LXIX | 203 |

LXXI | 205 |

LXXII | 207 |

LXXIII | 211 |

LXXXII | 242 |

LXXXIII | 244 |

LXXXIV | 246 |

LXXXV | 249 |

LXXXVI | 251 |

LXXXVII | 252 |

LXXXVIII | 254 |

LXXXIX | 258 |

XC | 261 |

XCI | 263 |

XCII | 264 |

XCIII | 266 |

XCIV | 267 |

XCV | 271 |

XCVI | 273 |

XCVII | 277 |

XCVIII | 280 |

XCIX | 285 |

C | 289 |

CI | 293 |

CII | 295 |

CIII | 306 |

CIV | 315 |

CV | 317 |

CVI | 321 |

CVII | 324 |

CVIII | 334 |

CIX | 341 |

CX | 345 |

CXI | 348 |

CXII | 352 |

CXIII | 355 |

CXIV | 358 |

CXV | 361 |

CXVI | 363 |

CXVII | 370 |

CXVIII | 396 |

398 | |

CXX | 399 |

CXXII | 400 |

CXXIII | 404 |

CXXIV | 407 |

CXXV | 409 |

CXXVI | 410 |

CXXVII | 413 |

CXXVIII | 416 |

CXXIX | 422 |

CXXX | 430 |

CXXXI | 431 |

CXXXII | 433 |

CXXXIII | 435 |

CXXXIV | 437 |

CXXXV | 440 |

CXXXVI | 444 |

CXXXVII | 447 |

CXXXVIII | 452 |

CXXXIX | 454 |

457 | |

### Common terms and phrases

action algebraic analytic assume automorphism blowup Brieskorn bundle canonical cohomology complete intersection complex components computed cone consider construction coordinates Corollary corresponding Coxeter-Dynkin diagram critical points critical values curve f cusps defined deformation denote diagram dimension element embedding equivalent equivariant example fiber fibration finite formula function Geometry germ given hence Hodge numbers holomorphic homeomorphism homology hyperbolic hypersurface ideal induced integral invariants irreducible isolated singularity isomorphic Legendrian links Lemma Math Milnor Milnor fibre Milnor lattice Milnor number mixed Hodge structure module moduli space monodromy group monomial morphism multiplicity obtain oriented pair Picard-Lefschetz formula plane curve plane curve singularities polynôme polynomial projective Proposition quotient resolution resolution of singularities resp respectively Section sequence shadow smooth space strict transform subset subspace surface surjective tangent theory topological Torelli theorem toric trivial vanishing cycles variety vector fields Zariski zero