Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Streszczenie

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.