Finiteness theorem on Blow-semialgebraic triviality for a family of 3-dimensional algebraic sets

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dc.creatorKoike, Satoshi
dc.date2007-11-19
dc.date.accessioned2026-07-07T08:43:42Z
dc.date.available2026-07-07T08:43:42Z
dc.descriptionIn this paper we introduce the notion of Blow-semialgebraic 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 3-dimensional 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 Blow-semialgebraic trivialisation consistent with a compatible filtration. We show a similar result on finiteness also for a Nash family of 3-dimensional Nash sets through the Artin-Mazur theorem. As a corollary of the arguments in their proofs, we have a finiteness theorem on semialgebraic types of polynomial mappings from the 2-dimensional Euclidean space to the p-diemnsional Euclidean space.
dc.description38 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0711.2862
dc.identifierhttp://arxiv.org/abs/0711.2862
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142407
dc.subjectAlgebraic Geometry
dc.subject32S15, 14P10
dc.titleFiniteness theorem on Blow-semialgebraic triviality for a family of 3-dimensional algebraic sets
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