desing v1.2 Singular Library for Desingularization of Subschemes of Smooth Varieties after O. Villamayor and S. Encinas by Josef Schicho and Gabor Bodnar ABOUT ----- The package is an implementation of the algorithm extracted from the constructive proof of the existence of embedded resolution of singularities for hypersurfaces, published by Villamayor (1989). The main source of his proof for this work was the paper: S. Encinas and O. Villamayor, A course on constructive desingularization and equivariance, In Resolution of singularities, A research textbook in tribute to Oscar Zariski, editors H. Hauser, J. Lipman, F. Oort and A. Quiros, Progress in Mathematics 181, Birkhauser (2000). The fundamentals of the implementation was published in: G. Bodnar and J. Schicho, Automated resolution of singularities for hypersurfaces, Journal of Symbolic Computation 30(4): 401-428, Academic Press (2000). Efficient computational methods for certain subtasks of the algorithm were published in: G. Bodnar, J. Schicho: Two computational techniques for singularity resolution, Journal of Symbolic Computation, 32(1-2):39-54, (2001). The implementation works in arbitrary dimensions. The package offers several advanced features beside its basic functionality. Please consult the manual and the online help for more information on these. VERSION ------- This is version 1.2 Release feature history: 1.2 - the speedup strategy of normal crossings test has been rewritten, the corresponding feature is turned on by default now, - computation of global sections of ideal sheaves on the variety W' (in the computed resolution W'->W) is introduced, - computation of integral closure of ideals via their principalization, - minor bugfixes. 1.1.1 - a bug is removed from the computation of suitable covers in 'case 5' in resolves. - using FOCUS is made optional via the DCFG[DCFOCUS] config variable. 1.1 - the explicit normal crossings test (NCTEST) has been finalized and made effective (the theoretical background is to be presented in a forthcoming paper), - if one wants to resolve singularities of reducible algebraic sets, it is possible to build superposed resolutions of the irreducible components by a new resolution strategy which achieves embedded resolution by a final component separation phase (the theoretical background is to be presented in a forthcoming paper), - the resolution stops now always when an embedded resolution is reached and no unnecessary finishing blowing ups are computed, - minor bugfixes. 1.0 - basic functionality (resolution of hypersurfaces and pure dimensional varieties, principalization of ideals), - text output for debugging, - HTML exporter, - applying the standard basis computation facility of Singular in semilocal rings (optional), - applying the "normal crossing test" for nonsingular hypersurfaces to avoid unnecessary blowing ups (optional), - in 1.0.1 bugs are removed from singular locus computation for weighted objects and from equi-order computation, and the transform of tagged objects along blowing ups is modified, - in 1.0.2 a bug is removed from the blowup routine for the localized version of the algorithm so that the charts of the blowing up variety are generated in the right order now, moreover in the monomial case the localization became the usual one. The development of the algorithm is being continued and new versions, optimizations are to be released on the web site: http://www.risc.uni-linz.ac.at/projects/basic/adjoints/blowup REQUIREMENTS ------------ The package is written for Singular version 2.0, it is strongly recommended to use Singular 2-0-6 (or higher). INSTALLATION ------------ The archive can be unpacked on a unix system using the command: tar xfz desingv1.1.1s.tar.gz It will create a directory named "desingv1.1.1s" with the content below. Since Singular libraries are loaded as source code, no special preparation is required. Just copy the file "desing.lib" into the "LIB/" directory of your installation of Singular, then it can be loaded as any other singular library. The content of the archive is the following: desing.lib the library source code GPL the text of GNU General public license README this file maunal.ps the manual of the package input.examples a few examples to illustrate how to use the package COMMENTS -------- For more detailed description of the HTML output, and other topics related to the algorithm, please visit the web page http://www.risc.uni-linz.ac.at/projects/basic/adjoints/blowup Bug reports, feedbacks should be sent to adjoints@risc.uni-linz.ac.at COPYRIGHT NOTICE ---------------- Copyright (C) 2002-2004 by Research Institute for Symbolic Computation Johannes Kepler University A-4040 Linz, Austria. The system is freely distributed under the GNU GPL with the following additional conditions: Any research activity which uses `desing' should cite the authors and the system explicitly. New users are encouraged to notify the authors via the email address adjoints@risc.uni-linz.ac.at to be kept informed about the further development and releases of the system. NOTE: This system is not a part of the standard set of Singular libraries.