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2003-06-24Buch DOI: 10.18452/2603
A first approach to generalized polar varieties
dc.contributor.authorBank, Bernd
dc.contributor.authorGiusti, Marc
dc.contributor.authorHeintz, Joos
dc.contributor.authorPardo, Luis-Miguel
dc.date.accessioned2017-06-15T17:41:42Z
dc.date.available2017-06-15T17:41:42Z
dc.date.created2005-11-03
dc.date.issued2003-06-24
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3255
dc.description.abstractLet W be a closed algebraic subvariety of the n-dimensional projective space over the complex or real numbers and suppose that W is non--empty and equidimensional. In this paper we generalize the classic notion of polar variety of W associated with a given linear subvariety of the ambient space of W. As particular instances of this new notion of generalized polar variety we reobtain the classic ones and two new types of polar varieties, called {\it dual} and (in case that W is affine) {\it conic}. We show that for a generic choice of their parameters the generalized polar varieties of W are empty or equidimensional and, if W is smooth, that their ideals of definition are Cohen--Macaulay. In the case that the variety W is affine and smooth and has a complete intersection ideal of definition, we are able, for a generic parameter choice, to describe locally the generalized polar varieties of W by explicit equations. Finally, we use this description in order to design a new, highly efficient elimination procedure for the following algorithmic task: In case, that the variety W is \Q-definable and affine, having a complete intersection ideal of definition, and that the real trace of W is non--empty and smooth, find for each connected component of the real trace of W a representative point.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectcomplexityeng
dc.subjectgeometric degreeeng
dc.subjectarithmetic networkeng
dc.subjectGeometry of polar varieties and its generalizationseng
dc.subjectreal polynomial equation solvingeng
dc.subjectelimination procedureeng
dc.subjectarithmetic circuiteng
dc.subject.ddc510 Mathematik
dc.titleA first approach to generalized polar varieties
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052373
dc.identifier.doihttp://dx.doi.org/10.18452/2603
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages39
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2003
local.edoc.container-issue5
local.edoc.container-year2003
local.edoc.container-erstkatid2075199-0

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