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Abstract

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.