Remarks on the generalized index of an analytic improper intersection

Krzysztof Jan Nowak¹

¹ Institute of Mathematics Jagiellonian University Reymonta 4, 30-059 Kraków, Poland

Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 47-53.

Résumé

This article continues the investigation of the analytic intersection algorithm from the perspective of deformation to the normal cone, carried out in the previous papers of the author [7, 8, 9]. The main theorem asserts that, given an analytic set $V$ and a linear subspace $S$, every collection of hyperplanes, admissible with respect to an algebraic bicone $B$, realizes the generalized intersection index of $V$ and $S$. This result is important because the conditions for a collection of hyperplanes to be admissible with respect to $B$ are of geometric nature: it is not necessary to analyse the embedded components of the intersections involved, but only the supports of the intersections of $B$ with successive hyperplanes.

Détail

DOI : 10.4064/ap81-1-4

Keywords: article continues investigation analytic intersection algorithm perspective deformation normal cone carried out previous papers author main theorem asserts given analytic set linear subspace every collection hyperplanes admissible respect algebraic bicone realizes generalized intersection index result important because conditions collection hyperplanes admissible respect geometric nature necessary analyse embedded components intersections involved only supports intersections successive hyperplanes