Finiteness theorem on Blowsemialgebraic triviality for a family of 3dimensional algebraic sets
Abstract
In this paper we introduce the notion of Blowsemialgebraic triviality consistent with a compatible filtration for an algebraic family of algebraic sets, as an equisingularity for real algebraic singularities. Given an algebraic family of 3dimensional algebraic sets defined over a nonsingular algebraic variety, we show that there is a finite subdivision of the parameter algebraic set into connected Nash manifolds over which the family admits a Blowsemialgebraic trivialisation consistent with a compatible filtration. We show a similar result on finiteness also for a Nash family of 3dimensional Nash sets through the ArtinMazur theorem. As a corollary of the arguments in their proofs, we have a finiteness theorem on semialgebraic types of polynomial mappings from the 2dimensional Euclidean space to the pdiemnsional Euclidean space.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2862
 Bibcode:
 2007arXiv0711.2862K
 Keywords:

 Mathematics  Algebraic Geometry;
 32S15;
 14P10
 EPrint:
 38 pages, 1 figure