Automated Resolution of Singularities for Hypersurfaces

We give the description of an algorithm for the resolution of singularities, in the case of hypersurfaces in characteristic zero, based on Villamayor?s stratifying function. The algorithm is implemented in Maple.

[1]  S. Encinas,et al.  Good points and constructive resolution of singluarities , 1998 .

[2]  Carlo Traverso,et al.  Effective methods in algebraic geometry , 1991 .

[3]  Herwig Hauser,et al.  Seventeen Obstacles for Resolution of Singularities , 1998 .

[4]  Franz Winkler,et al.  A p-Adic Approach to the Computation of Gröbner Bases , 1988, J. Symb. Comput..

[5]  N. Bose Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory , 1995 .

[6]  Josef Schicho,et al.  A Computer Program for the Resolution of Singularities , 2000 .

[7]  H. Hironaka Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II , 1964 .

[8]  Villamayor U. Orlando Introduction to the Algorithm of Resolution , 1996 .

[9]  Orlando E. Villamayor,et al.  Constructiveness of Hironaka's resolution , 1989 .

[10]  U Villamayor,et al.  Patching local uniformizations , 1992 .

[11]  D. Eisenbud Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[12]  Santiago Encinas,et al.  A Course on Constructive Desingularization and Equivariance , 2000 .

[13]  Joseph Lipman,et al.  Desingularization of two-dimensional schemes , 1978 .

[14]  Oscar Zariski,et al.  The Reduction of the Singularities of an Algebraic Surface , 1939 .

[15]  Oscar Zariski,et al.  Reduction of the Singularities of Algebraic Three Dimensional Varieties , 1944 .

[16]  Edward Bierstone,et al.  Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant , 1995 .

[17]  Edward Bierstone,et al.  A simple constructive proof of Canonical Resolution of Singularities , 1991 .