Singularities and computer algebra / edited by Christoph Lossen & Gerhard Pfister.

Format:

Book

Contributor:

Lossen, Christoph.

Pfister, Gerhard, 1947-

Series:

London Mathematical Society lecture note series ; 324.

London Mathematical Society lecture note series ; 324

Language:

English

Subjects (All):

Geometry, Algebraic.

Singularities (Mathematics).

Physical Description:

xxxvi, 371 pages : illustrations, portrait ; 23 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2006.

Contents:

Aspects of Gert-Martin Greuel's Mathematical Work / Christoph Lossen, Gerhard Pfister xvii

Exterior Algebra Methods for the Construction of Rational Surfaces in the Projective Fourspace / Hirotachi Abo, Frank-Olaf Schreyer 1

1 The Exterior Algebra Method 3

2 Construction 5

Superisolated Surface Singularities / Enrique Artal Bartolo, Ignacio Luengo, Alejandro Melle Hernandez 13

1 Superisolated Surface Singularities 14

2 Deformations 20

3 Zariski Pairs 21

4 Monodromy Conjecture 23

5 SIS Singularities with Rational Homology Sphere Links and Rational Cuspidal Curves 27

Linear Free Divisors and Quiver Representations / Ragnar-Olaf Buchweitz, David Mond 41

2 Linear Free Divisors 43

3 Representations of Quivers 44

4 The Fundamental Exact Sequence 48

5 Deformations of Representations 49

6 A Criterion for D to be a Linear Free Divisor 56

8 Equations for D 65

9 An Interlude from Commutative Algebra 71

10 The Case of E[subscript 8] with the Centre as Only Sink 73

Derived Categories of Modules and Coherent Sheaves / Yuriy A. Drozd 79

2 Finite Dimensional Algebras 85

3 Nodal Rings 98

4 Projective Curves 114

Monodromy / Wolfgang Ebeling 129

1 The Monodromy Operator 130

2 Computation of Monodromy 133

3 Zeta Function 135

4 Spectrum 139

5 Monodromy and the Topology of the Singularity 142

Algorithmic Resolution of Singularities / Anne Fruhbis-Kruger, Gerhard Pfister 157

1 Blowing Up 159

2 The b-Singular Locus and Basic Objects 162

3 The Monomial Case 167

4 The Tower of a Basic Object 168

5 Some Remarks on Applications 180

Newton Polyhedra of Discriminants: A Computation / Evelia Garcia Barroso, Bernard Teissier 185

1 Plane Branches, Semigroups and Monomial Curves 187

2 The Discriminant 192

3 Curves with Two Characteristic Pairs 194

4 A Question of Genericity 204

5 The Information is Constant 208

Depth and Differential Forms / Helmut A. Hamm 211

1 A de Rham Lemma for Complete Intersections 213

2 Application: Complete Intersections in P[subscript m] 215

3 Relation to Residues 216

4 A Generalized Akizuki-Nakano Theorem 217

5 A Preliminary Lefschetz Theorem for Differential Forms 220

6 De Rham Cohomology and Singular Cohomology 222

7 A Lefschetz Theorem for Differential Forms on Local Complete Intersections 226

8 Logarithmic de Rham Cohomology and the Gysin Sequence 227

The Geometry of the Versal Deformation / Le Dung Trang 233

1 On the Local Topology of Isolated Hypersurface Singularities 234

3 Geometry of a Versal Deformation 238

4 Geometry of the Discriminant 242

5 Open Problems 244

21 Years of SINGULAR Experiments in Mathematics / Christoph Lossen, Hans Schonemann 247

1 The Early Years 249

2 Applications in Singularity Theory 252

3 The Latest Features: SINGULAR 3 262

The Patchworking Construction in Tropical Enumerative Geometry / Eugenii Shustin 273

2 Patchworking of Curves on Toric Surfaces 275

3 Patchworking of Curves on Arbitrary Surfaces 291

4 Nodal Deformations of Non-Planar Isolated Curve Singularities 294

Adjunction Conditions for One-Forms on Surfaces in Projective Three-Space / Joseph H.M. Steenbrink 301

1 Differentials on Spaces with Quotient Singularities 302

2 The Filtered de Rham Complex 303

3 Barlet Differentials 304

4 Smoothing: the Specialization Sequence 305

5 Local Comparison 306

6 Application to Projective Hypersurfaces 310

Sextic Surfaces with Ten Triple Points / Jan Stevens 315

1 Nine Triple Points 316

2 Families with Ten Triple Points 319

Some Problems on Lagrangian Singularities / Duco van Straten 333

1 Definitions and Examples of Lagrangian Singularities 333

2 Algebraic and Geometric Aspects 336

3 Deformations and Rigidity 340

4 The [delta]-constant Stratum 343

Topology, Geometry, and Equations of Normal Surface Singularities / Jonathan Wahl 351

2 The Basics of Normal Surface Singularities 353

3 Some Cases when Topology Implies Nice Geometry 356

4 Universal Abelian Covers of Singularities with QHS Links 358

5 Splice Diagrams and Complete Intersections of Splice Type - ZHS Case 360

6 Generalized Splice Diagrams and CIST's 365

7 Okuma's Theorem and Further Questions 368.

Notes:

"From 18 to 20 October 2004, a conference 'Singularities and computer algebra' was held at the University of Kaiserslautern on the occasion of Gert-Martin Greuel's 60th birthday... The papers of this volume concern ten of the invited lectures, supplemented by four articles which are written by participants of the conference"--Pref.

Includes bibliographical references.

ISBN:

0521683092

OCLC:

65763553

Publisher Number:

9780521683098