Computation of Milnor numbers and critical values at infinity

Details Computation of Milnor numbers and critical values at infinity Computation of Milnor numbers and critical values at infinity

2003-09-19

arxiv.org/abs/math/0309322v1

Journal of Symbolic Computation (2004, vol. 38, 1417-1427)

Mathematics

Algebraic Geometry

9 pages.To download the libraries for Singular see http://www-gat.univ-lille1.fr/~bodin/

Scientific paper

10.1016/j.jsc.2004.04.003

We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the critical values at infinity, and the Milnor numbers at infinity for all irregular fibers. Then for a family of polynomials we detect parameters where the topology of the polynomials can change. Implementation and examples are given with the computer algebra system Singular.

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