Singularities and Computer Algebra

1. Front Matter

   Pages i-xiv

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2. On Some Conjectures About Free and Nearly Free Divisors

   • Enrique Artal Bartolo, Leire Gorrochategui, Ignacio Luengo, Alejandro Melle-Hernández

   Pages 1-19

3. A Classification Algorithm for Complex Singularities of Corank and Modality up to Two

   • Janko Böhm, Magdaleen S. Marais, Gerhard Pfister

   Pages 21-46

4. Linear Resolutions of Powers and Products

   • Winfried Bruns, Aldo Conca

   Pages 47-69

5. Minors and Categorical Resolutions

   • Igor Burban, Yuriy Drozd, Volodymyr Gavran

   Pages 71-95

6. Higher-Order Spectra, Equivariant Hodge–Deligne Polynomials, and Macdonald-Type Equations

   • Wolfgang Ebeling, Sabir M. Gusein-Zade

   Pages 97-108

7. μ-Constant Monodromy Groups and Torelli Results for Marked Singularities, for the Unimodal and Some Bimodal Singularities

   • Falko Gauss, Claus Hertling

   Pages 109-146

8. Divisor Class Groups of Affine Complete Intersections

   • Helmut A. Hamm

   Pages 147-160

9. Möbius Strips, Knots, Pentagons, Polyhedra, and the SURFER Software

   • Stephan Klaus

   Pages 161-172

10. Seiberg–Witten Invariant of the Universal Abelian Cover of \({S_{-p/q}^{3}(K)}\)

    • József Bodnár, András Némethi

    Pages 173-197

11. A Method to Compute the General Neron Desingularization in the Frame of One-Dimensional Local Domains

    • Adrian Popescu, Dorin Popescu

    Pages 199-222

12. Coherence of Direct Images of the De Rham Complex

    • Kyoji Saito

    Pages 223-256

13. Remarks on the Topology of Real and Complex Analytic Map-Germs

    • José Seade

    Pages 257-274

14. On Welschinger Invariants of Descendant Type

    • Eugenii Shustin

    Pages 275-304

15. Milnor Fibre Homology via Deformation

    • Dirk Siersma, Mihai Tibăr

    Pages 305-322

16. Some Remarks on Hyperresolutions

    • J. H. M. Steenbrink

    Pages 323-327

17. Deforming Nonnormal Isolated Surface Singularities and Constructing Threefolds with \(\mathbb{P}^{1}\) as Exceptional Set

    • Jan Stevens

    Pages 329-351

18. On a Theorem of Greuel and Steenbrink

    • Duco van Straten

    Pages 353-364

19. A Kirwan Blowup and Trees of Vector Bundles

    • G. Trautmann

    Pages 365-389

This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra.
Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists.
The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.

• singularity theory
• algebraic geometry
• topology
• complex analysis
• computer algebra
• ordinary differential equations

• Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

  Wolfram Decker, Gerhard Pfister, Mathias Schulze

Wolfram Decker is a professor in the Department of Mathematics at the TU Kaiserslautern, Germany.
Gerhard Pfister is a professor in the Department of Mathematics at the TU Kaiserslautern, Germany.
Mathias Schulze is a professor in the Department of Mathematics at the TU Kaiserslautern, Germany.

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