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The Okounkov body is a construction which, to an effective divisor D on an n-dimensional algebraic variety X, associates a convex body Δ(D) in the n-dimensional Euclidean space R n . It may be seen as a generalization of the moment polytope of an ample divisor on a toric variety, and it encodes rich numerical information about the divisor D. When constructing the Okounkov body, an intermediate product is a lattice semigroup Γ(D) ⊂ N n+1 , which we will call the Okounkov semigroup. Recently itdoi:10.4310/mrl.2017.v24.n2.a8 fatcat:w3vygyzlgzhkjochjnezrb3mdu