{"product_id":"geometry-of-the-semigroup-z_-0-n-and-its-applications-to-combinatorics-algebra-and-differential-equations-von-sergey-chulkov-und-askold-khovanskii","title":"Geometry of the Semigroup Z_(≥0)^n and its Applications to Combinatorics, Algebra and Differential Equations","description":"\n                                \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                                \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                                \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                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642309878\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783642309878","offer_id":58942692262213,"sku":"9783642309878","price":42.75,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/noimage.png?v=1613155958","url":"https:\/\/shop.autorenwelt.de\/en\/products\/geometry-of-the-semigroup-z_-0-n-and-its-applications-to-combinatorics-algebra-and-differential-equations-von-sergey-chulkov-und-askold-khovanskii","provider":"Autorenwelt Shop","version":"1.0","type":"link"}