{"product_id":"9783642309878","title":"Geometry of the Semigroup Z_(≥0)^n and its Applications to Combinatorics, Algebra and Differential Equations","description":"\u003ch1\u003eGeometry of the Semigroup Z_(≥0)^n and its Applications to Combinatorics, Algebra and Differential Equations\u003c\/h1\u003e\u003ch3\u003eSergey Chulkov | Askold Khovanskii | Sergey Chulkov\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Geometry \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003eThis 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. \u003c\/p\u003e\n\u003cp\u003eThe 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. \u003c\/p\u003e\n\u003cp\u003eThe 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.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e01 July 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Berlin Heidelberg\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783642309878\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003eHardback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":51323179040908,"sku":"9783642309878","price":44.96,"currency_code":"USD","in_stock":true}],"url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783642309878","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}