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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 |
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