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TitleOn the probability distribution of singular varieties of given corank
Author(s) Carlos Beltrán, Luis Miguel Pardo
TypeArticle in Journal
AbstractWe exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank. We also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations. We finally state a new and sharp technique of the Geometry of Numbers. Using this technique we show that rational systems of multivariate polynomial equations are equidistributed with respect to singular systems having a critical zero of given corank.
KeywordsPolynomial equation solving, Condition number, Discrepancy bounds
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717106000629
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number12
Pages4 - 29
Year2007
NoteEffective Methods in Algebraic Geometry (MEGA 2005)
Edition0
Translation No
Refereed No
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