Remarks on the generalized index of an analytic improper intersection

Volume 81 / 2003

Krzysztof Jan Nowak Annales Polonici Mathematici 81 (2003), 47-53 MSC: 14C17, 32S10, 32C25, 32B10. DOI: 10.4064/ap81-1-4

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.

Authors

  • Krzysztof Jan NowakInstitute of Mathematics
    Jagiellonian University
    Reymonta 4, 30-059 Kraków, Poland
    e-mail

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