**Proceedings of Symposia in Pure Mathematics**

Volume: 40;
1983;
676 pp;
Hardcover

MSC: Primary 14;
Secondary 32; 57; 58

Print ISBN: 978-0-8218-1450-5

Product Code: PSPUM/40.1

List Price: $102.00

Individual Member Price: $81.60

**Electronic ISBN: 978-0-8218-9331-9
Product Code: PSPUM/40.1.E**

List Price: $102.00

Individual Member Price: $81.60

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# Singularities, Part 1

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*Peter Orlik*

#### Table of Contents

# Table of Contents

## Singularities, Part 1

- Table of Contents: Part 1 v6 free
- Preface xvii18 free
- List of participants xxiii24 free
- Desingularization of plane curves 128 free
- Zeros of holomorphic vector fields and the Gysin homomorphism 4774
- On the graded rings associated to holomorphic vector fields with exactly one zero 5582
- Some open problems in the theory of singularities 5784
- Complex surfaces of small homotopy type 7198
- Homeomorphy classification of normal surfaces in P[sub(3)] with C[sub(*)]-action 81108
- Minimal free resolutions of Gorenstein local rings with small multiplicity 105132
- Analytic equivalence of isolated hyper surface singularities defined by homogeneous polynomials 111138
- An application of singularity theory to nonlinear elliptic partial differential equations 119146
- Algebras of composite differentiable functions 127154
- The extension problem and related themes in differential analysis 137164
- On global extensions of Dynkin diagrams and singular surfaces of the topological type of P[sup(2)] 145172
- Milnor lattices and Dynkin diagrams 153180
- On the topology of polynomial hyper-surfaces 167194
- Genericity of caustics by reflexion 179206
- Envelopes, duality and contact structures 195222
- Bifurcation involving the hexagonal lattice 203230
- On saturations of curve singularities (any characteristic) 211238
- A note on the classes [Skl (f)] 221248
- Differential maps with small critical set 225252
- The unfolding and determinacy theorems for subgroups of a and k 233260
- Topological triviality in versal unfoldings 255282
- Newton filtrations, monomial algebras and nonisolated and equivariant singularities 267294
- Contact germs from the plane to the plane 277304
- Weyl groups and Cremona transformations 283310
- Genericity and smooth finite determinacy 295322
- A naive guide to mixed Hodge theory 313340
- The low-dimensional topology of singularities 321348
- On the monodromy groups of singularities 327354
- Rational curves with cusps 337364
- Mixed Hodge structures 345372
- Special polars and curves with one place at infinity 353380
- Another view of critical point theory 361388
- Some results on Poincare duality 373400
- Some essential valuations in the resolution of singularities 381408
- Derivations and smooth discriminant 385412
- Singularities of period maps and the weak global Torelli problem 391418
- The Thorn polynomial of Σ[sup(1111)] 399426
- The structure of Ta (f), classification and an application to differential geometry 409436
- Multiple points and associated ramification loci 429456
- Equivalence theorems in global singularity theory 439466
- Hilbert scheme as flattener 449476
- Differential in variance of multiplicity 453480
- Classification des singularites isolees simples d'intersections completes 457484
- Finding the nondegenerate quadratic singularities 495522
- A discussion of symmetry and symmetry breaking 499526
- Stratified Morse theory 517544
- On the topology of smoothable singularities 535562
- Lefschetz theorems for singular varieties 547574
- Stratification via corank one projections 559586
- An algorithm of construction of the semiuniversal deformation of an isolated singularity 567594
- Limites de normales, conditions de Whitney et éclatement d'Hironaka 575602
- Computation of some projective invariants 585612
- Deforming complete intersection Artin algebras. Appendix: Hilbert function of C[x, y]/I 593620
- Duality for Riemannian foliations 609636
- Normally flat deformations of rational and minimally elliptic singularities 619646
- The topology of real algebraic sets 641668
- Differential forms and the fundamental group of the complement of hypersurfaces 655682
- Questions about the proof of the hard Lefschetz theorem 663690
- Metric study of the neighbourhood of a singularity 669696