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In algebraic geometry, a Newton–Okounkov body, also called an Okounkov body, is a convex body in Euclidean space associated to a divisor (or more generally a linear system) on a variety. The convex geometry of a Newton–Okounkov body encodes (asymptotic) information about the geometry of the variety and the divisor. It is a far generalization of the notion of the Newton polytope of a projective toric variety. It was introduced (in passing) by Andrei Okounkov in his papers in the late 1990s and early '00s. Okounkov’s construction relies on an earlier result of Askold Khovanskii on semigroups of lattice points. Later Okounkov’s construction was generalized and systematically developed in the papers of Lazarsfeld and Mustata as well as Kaveh and Khovanskii. Beside Newton polytopes of toric varieties, several polytopes appearing in representation theory (such as Gelfand–Zetlin polytopes and string polytopes of Littelmann and Berenstein–Zelevinsky) can be realized as special cases of Newton–Okounkov bodies. ==References== * * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Newton–Okounkov body」の詳細全文を読む スポンサード リンク
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