Pyramids and monomial blowing-ups

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dc.creatorSoto, M. J.
dc.creatorVicente, José L.
dc.date2004-09-23
dc.date.accessioned2026-07-07T05:12:30Z
dc.date.available2026-07-07T05:12:30Z
dc.descriptionWe show that a convex pyramid in R^n with apex at 0 can be brought to the first quadrant by a finite sequence of monomial blowing-ups if and only if its intersection with the opposite of the first quadrant is 0. The proof is non-trivially derived from the theorem of Farkas-Minkowski. Then, we apply this theorem to show how the Newton diagrams of the roots of any Weierstrass polynomial are contained in a pyramid of this type. Finally, if n = 2, this fact is equivalent to the Jung-Abhyankar theorem.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0409446
dc.identifierhttp://arxiv.org/abs/math/0409446
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72597
dc.subjectCommutative Algebra
dc.subjectOptimization and Control
dc.subject15A39 (Primary), 13H99 (Secondary)
dc.titlePyramids and monomial blowing-ups
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