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A’Campo-Neuen, J. Hausen and S. AG/0005083. [14] S. Aguzzoli and D. Mundici, An algorithmic desingularization of 3-dimensional toric varieties, Tohoku Math. J. 46 (1994), 557–572. [15] K. Altmann, One-parameter families containing three-dimensional toric Gorenstein singularities, in Explicit Birational Geometry of 3-Folds (A. Corti and M. Reid, editors), London Math. Soc. Lecture Notes Ser. 281, Cambridge Univ. Press, Cambridge, 2000, 21–50; alg-geom/9609006. [16] K. Altmann, Singularities arising from lattice polytopes, in Singularity Theory (Liverpool, 1996) (B.

K[Z+ ⊕ Zn−1 ] ∼ = K[Y, Z1±1 , . . , Zn−1 Each of them is integrally closed in its field of fractions QF(K[L]). If S is normal, then one has a splitting S = S0 ⊕ S as discussed above. It induces an isomorphism K[S] = K[S0 ] ⊗ K[S ]. Therefore K[S] is a Laurent polynomial extension of K[S ]. Since Laurent polynomial extensions preserve essentially all ring-theoretic properties, it is in general no restriction to assume that S is positive (if it is normal). Monomial prime ideals. — The prime ideals in K[S] that are generated by monomials can be easily described geometrically.

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