Singularities and computer algebra : Festschrift for Gert-Martin Greuel on the occasion of his 70th birthday / edited by Wolfram Decker, Gerhard Pfister, Mathias Schulze.

Format:

Book

Contributor:

Decker, W., Editor.

Pfister, Gerhard, Editor.

Schulze, Mathias., Editor.

Language:

English

Subjects (All):

Geometry, Algebraic.

Differential equations.

Algebraic Geometry.

Ordinary Differential Equations.

Local Subjects:

Algebraic Geometry.

Ordinary Differential Equations.

Physical Description:

1 online resource (XIV, 389 p. 55 illus., 19 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

Gert-Martin Greuel’s work, Duco van Straten

Divisor class groups of affine complete intersections, Helmut Hamm

Rational plane quartics and K3 surfaces, Viktor Kulikov

Remarks on the Lê–Greuel formula for the Milnor number, José Seade

Bi-Lipschitz regular complex space are regular, Lê Dũng Tráng

Enumeration of real algebraic curves, Eugenii Shustin

A real analytic cell complex for the braid group, Norbert A’Campo

Old and new regarding the Seiberg–Witten invariant conjecture, Andras Nemethi

Multiplication by f in the Jacobian algebra as bindings in the spectrum of a hypersurface with an isolated singularity, Xavier Gomez-Mont

Marked singularities, their moduli spaces, and atlases of stokes data, Claus Hertling

Depth and regularity of powers of sums of ideals, Ngô Việt Trung

Deforming non-normal isolated surface singularities, Jan Stevens

Vanishing topology of Cohen–Macaulay codimension 2 3-folds, Anne Frühbis-Krüger

Equisingular moduli of rational surface singularities, Jonathan Wahl

Algebraic bubbling for vector bundles on surfaces, Günter Trautmann

Recombination formulas for the spectrum of plane curve singularities, Dmitry Kerner

Minors and categorical resolutions, Yuri Drozd

Resolutions of cubical varieties, Joseph Steenbrink

Hypersurfaces with 1-dimensional singularities, Dirk Siersma

Higher order Euler characteristics, their generalizations and generating series, Sabir Gusein-Zade

Torsion free sheaves on degenerate elliptic curves and the classical Yang–Baxter equation, Igor Burban

Normal lattice polytopes, Winfried Bruns

Möbius strips, knots, pentagons, polyhedra and the SURFER, Stephan Klaus

Computational D-module theory and singularities, Viktor Levandovskyy

Orbifold zeta functions for dual invertible polynomials, Wolfgang Ebeling

Polarity maps, singular subschemes, and applications, Antonio Campillo

Parallelisation in Singular, Hans Schönemann

Milnor number, discriminant and unfolding of isolated singularities in positive characteristic, Duc Nguyen.

Notes:

Includes bibliographical references.

ISBN:

3-319-28829-6