COMPUTATION OF MILNOR NUMBERS AND CRITICAL

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Niveau: Supérieur, Doctorat, Bac+8
COMPUTATION OF MILNOR NUMBERS AND CRITICAL VALUES AT INFINITY ARNAUD BODIN Abstra t. We des ribe how to ompute topologi al obje ts asso iated to a om- plex polynomial map of n > 2 variables with isolated singularities. These obje ts are: the aÆne riti al values, the aÆne Milnor numbers for all irregular bers, the riti al values at innity, and the Milnor numbers at innity for all irregular bers. Then for a family of polynomials we dete t parameters where the topology of the polynomials an hange. Implementation and examples are given with the omputer algebra system Singular. 1. Introdu tion 1.1. Review on the lo al ase. Let g : C n ; 0 ! C ; 0 be a germ of polyno- mial map with isolated singularities. One of the most important topologi al obje t atta hed to g is its lo al Milnor number [Mi?: 0 = dim C C fx 1 ; : : : ; x n g=Ja (g) where Ja (g) = ( g x 1 ; : : : ; g x n ) is the Ja obian ideal of g. It is possible to ompute 0 with the help of a Grobner base.

  • polar urve

  • proje tion

  • lo al - onstant

  • ideal cbar

  • topologi ally

  • milnor numbers

  • ramanujam-timourian - onstant theorem

  • has strong


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