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OverviewThis vital contribution to the mathematical literature on combinatorics, algebra and differential equations develops two fundamental finiteness properties of the semigroup Z_(≥0)^n that elucidate key aspects of theories propounded by, among others, Hilbert and Kouchnirenko. The authors provide explanations for numerous results in the field that appear at first glance to be unrelated. The first finiteness property relates to the fact that Z_(≥0)^n can be represented in the form of a finite union of shifted n-dimensional octants, while the second asserts that any co-ideal of the semigroup can be represented as a finite, disjoint union of shifted co-ordinate octants. The applications of their work include proof that Hilbert’s implication that dimension d of the affine variety X equals the degree of Hilbert’s polynomial can be developed until its degree X equates to the leading coefficient of the Hilbert polynomial multiplied by d. The volume is a major forward step in this field. Full Product DetailsAuthor: Sergey Chulkov , Askold Khovanskii , Sergey ChulkovPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1st ed. 2024 ISBN: 9783642309878ISBN 10: 3642309879 Pages: 120 Publication Date: 26 August 2024 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Not yet available  This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Language: English Table of ContentsI Geometry and combinatorics of semigroups.- 1 Elementary geometry of the semigroup Zn>0.- 2 Properties of an ordered semigroup.- 3 Hilbert functions and their analogues.- II Applications: 4 Kouchnirenko`s theorem on number of solutions of a polynomial system of equations. On the Grothendieck groups of the semigroup of finite subsets of Zn and compact subsets of Rn.- 5 Differential Grobner bases and analytical theory of partial differential equations.- 6 On the Convergence of Formal Solutions of a System of Partial Differential Equations.- A Hilbert and Hilbert-Samuel polynomials and Partial Differential Equations.- ReferencesReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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