Singular

D.5.5 resolve_lib

Library:

resolve.lib

Purpose:

Resolution of singularities (Desingularization) Algorithm of Villamayor

Authors:

A. Fruehbis-Krueger, [email protected],
G. Pfister, [email protected]

References:

[1] 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)
[2] A.Bravo, S.Encinas, O.Villamayor: A Simplified Proof of Desingularisation and
Applications, Rev. Math. Iberoamericana 21 (2005), 349-458
(description of the algorithmic proof of desingularization in characteristic zero which underlies this implementation)
[3] A.Fruehbis-Krueger: Computational Aspects of Singularities, in J.-P. Brasselet, J.Damon et al.: Singularities in Geometry and Topology, World Scientific Publishing, 253--327 (2007)
(chapter 4 contains a detailed discussion on algorithmic desingularization and efficiency aspects thereof)

Procedures:

D.5.5.1 blowUp		computes the blowing up of the variety V(J) (considered as embedded in V(W)) in the (smooth) center V(C),
D.5.5.2 blowUp2		computes the blowing up of the variety V(J) in the (possibly singular) center V(C)
D.5.5.3 Center		computes 'Villamayor'-center for blow up
D.5.5.4 resolve		computes the desingularization of the variety V(J)
D.5.5.5 showBO		prints the content of a BO in more human readable form
D.5.5.6 presentTree		prints the final charts in more human readable form
D.5.5.7 showDataTypes		prints help text for output data types
D.5.5.8 blowUpBO		computes the blowing up of the variety V(BO[1]) in the center V(C). BO is a list (basic object), C is an ideal
D.5.5.9 createBO		creates basic object from input data
D.5.5.10 CenterBO		computes the center for the next blow-up of the given basic object
D.5.5.11 Delta		apply the Delta-operator of [Bravo,Encinas,Villamayor]
D.5.5.12 DeltaList		list of results of Delta^0 to Delta^bmax