desing - A computer program for resolution of singularities

Introduction to the Problem

A very short introduction to the area of resolution of singularities with a brief summary of the research history of the problem, following only the branch that led to our work.

About the Software
(Maple version, Singular version)

Facts about the desing package (requirements, current state, upcoming releases, etc.), with links to other Maple packages that desing uses.

Input-Output Descriptions
(Maple version, Singular version)

A brief description of the input and output specification of the program, with additional explanation of the structure of the data of the HTML export.


Links to a couple of examples. (The examples are provided by the 1.3 version of the package.)


A list of bibliographic entries related to: resolution of singularities, algorithms which play important role in desing (e.g. Gröbner basis), possible applications (e.g. computation of adjoints and surface parametrization).

Related Links

  • Josef Schicho (project leader). Research interests: constructive algebraic geometry, algebraic geometry, constructive analysis.
  • Gábor Bodnár. Research interests: computer algebra, constructive algebraic geometry.

All the versions of desing are available through the release history.


  • J.S.: Embedded Desingularization of Hypersurfaces after Villamayor, RISC Technical report 1997
  • G.B. & J.S.: A Computer Program for the Resolution of Singularities, in Resolution of Singularities, A research textbook in tribute to Oscar Zariski editors H. Hauser, J. Lipman, F. Oort, A. Quiros, Progress in Mathematics 181:231-238, Birkhauser 2000, (RISC Technical report version)
  • G.B. & J.S.: Automated Resolution of Singularities for Hypersurfaces, Journal of Symbolic Computation 30(4):401-428, Academic Press 2000, (RISC Technical report version)
  • G.B. & J.S.: Improvements of the Algorithm for Resolution of Singularities, RISC Technical report 2000
  • G.B. & J.S.: An Improved Algorithm for the Resolution of Singularities, in Proceedings of ISSAC 2000 editor C. Traverso, p. 29-36, ACM 2000.
  • G.B.: Algorithmic Resolution of Singularities, PhD Thesis, Johannes Kepler University, RISC-Linz 2000, (RISC Technical report version).
  • G.B. & J.S.: Two computational techniques for singularity resolution, Journal of Symbolic Computation 32(1-2):39-54, Academic Press 2001,
  • G.B. & J.S.: desing Manual
  • G.B.: Computation of blowing up centers, Journal of Pure and Applied Algebra, 179(3): 221-233, (2003).
  • G.B.: Algorithmic tests for the normal crossing property, In Proceedings of ADG 2002, F. Winkler editor, volume 2930 of LNAI, pages 1-20, Springer (2004).
  • G.B.: Efficient Desingularization of Reducible Algebraic Sets. In Proceedings of ISSAC 2004, J. Gutierrez editor, pages 35-41. ACM Press (2004).

Conference Talks

  • G.B & J.S.: On Algorithmic Desingularization of Hypersurfaces, presented at IMACS-ACA '98 (ps file)
  • G.B & J.S.: An Algorithm for Resolution of Singularities, presented at the Poster Session of ECCAD '99 (ps file)
  • G.B & J.S.: An Improved Algorithm for the Resolution of Singularities, ISSAC 2000, University of St. Andrews, 2000
  • G.B. & J.S.: Algorithmic Resolution of Singularities after Villamayor, Singularities of algebraic varieties and desingularization, University of Versailles-Ecole Polytechnique, France 2001


Sponsored by the Austrian Science Fund (FWF) through the project

Explicit Resolution and Related Methods in Algebraic Geometry and Number Theory

Project data

Project Leaders:
   Herwig Hauser, Josef Schicho

Project Members:
   Gábor Bodnár
   Sebastian Gann
   Dominik Zeillinger

   2002 Oct.- 2005 Sep.

   Austrian Science Fund (FWF)
   Pr. code: P15551

The official webpage of the project


The goal of the project is to develop theories and algorithms for solving problems related to the resolution of singularities in algebraic geometry and number theory. The three main subareas of research are the following.

Computing resolutions for various classes of varieties: The main punching line will be dimension two and three, both in characteristic zero and p. The reason is two-fold. First, we think that effective resolutions of 4-folds is practically too costly in terms of computing resources (although theoretically possible). Second, many interesting applications and phenomena happen to appear already in dimension two and three.
Solving problems in algebraic geometry related to resolution: This concerns the canonical class of an algebraic variety, in particular the parametrization problem for rational surfaces, the problem of finding rational and elliptic fibrations, and the problem of constructing canonical embeddings.
Solving problems in number theory related to resolution: The problems are related to p-adic completions and global fields, such as the computation of normal bases in number fields, or the existence problem of rational points on Del Pezzo surfaces.