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Singularities and Computer Algebra

Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday

  • Book
  • © 2017

Overview

Editors:
  1. Wolfram Decker

    1. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

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  2. Gerhard Pfister

    1. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

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  3. Mathias Schulze

    1. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

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  • Brings together recent original research and survey articles by leading experts in singularity theory and computer algebra

  • Highlights a large variety of techniques, ranging from theoretical methods to practical tools from computer algebra

  • Based on lectures given at a conference in honor of Gert-Martin Greuel on the occasion of his 70th birthday

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  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
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

    Wolfram Decker, Gerhard Pfister, Mathias Schulze

About the editors

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.

Bibliographic Information

  • Book Title: Singularities and Computer Algebra

  • Book Subtitle: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday

  • Editors: Wolfram Decker, Gerhard Pfister, Mathias Schulze

  • DOI: https://doi.org/10.1007/978-3-319-28829-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-28828-4Published: 05 April 2017

  • Softcover ISBN: 978-3-319-80435-4Published: 08 May 2018

  • eBook ISBN: 978-3-319-28829-1Published: 29 March 2017

  • Edition Number: 1

  • Number of Pages: XIV, 389

  • Number of Illustrations: 36 b/w illustrations, 19 illustrations in colour

  • Topics: Algebraic Geometry, Ordinary Differential Equations

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