Top
Back: list0
Forward: jungresolve
FastBack: resbin_lib
FastForward: surfacesignature_lib
Up: Experimental libraries
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.9 resjung_lib

Library:
resjung.lib
Purpose:
Resolution of surface singularities (Desingularization) by Jung's Algorithm
Authors:
Philipp Renner, philipp_renner@web.de
Anne Fruehbis-Krueger, anne@math.uni-hannover.de

Overview:
This library implements resolution of singularities by Jung's algorithm,
which is only applicable to surfaces and persues the following strategy:
1) project surface to the plane
2) resolve singularities of the branch locus
3) pull-back the original surface by this resolution morphism
4) normalize the resulting surface so that the remaining singularities
are of Hirzebruch-Jung type
5) resolve Hirzebruch-Jung singularities explicitly
Currently, the Hirzebruch-Jung singularities are resolved by calling
the procedure resolve from the library resolve.lib, because this is not
overly expensive and the original last step of Jung's algorithm is not
implemented yet.

References:
[1] Jung, H.: Darstellung der Funktionen eines algebraischen Koerpers zweier unabhaengigen Veraenderlichen x,y in der Umgebung x=a, y= b, Journal fuer Reine und Angewandte Mathematik 133,289-314 (1908)
(the origin of this method)
[2] J.Kollar: Lectures on Resolution of Singularities, Princeton University Press (2007)
(contains large overview over various known methods for curves and surfaces as well as a detailed description of the approach in the general case)

Procedures:

D.15.9.1 jungresolve  computes a resolution of the surface given by the ideal J using Jungs Method
D.15.9.2 clocus  computes the critical locus of the projection of V(J) onto the coordinate plane of the last two coordinates
D.15.9.3 embR  computes a strong embedded resolution of the plane curve V(C)
D.15.9.4 jungnormal  computes intermediate step in Jung's algorithm such that all singularities are of Hirzebruch-Jung type


Top Back: list0 Forward: jungresolve FastBack: resbin_lib FastForward: surfacesignature_lib Up: Experimental libraries Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-2, Oct 2010, generated by texi2html.