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The integral closure of ideals and the Newton filtration. (English) Zbl 0861.14048
Let \({\mathcal O}_n\) be the set of holomorphic germs \(g: (\mathbb{C}^n,0) \to(\mathbb{C},0)\) and let \(I\) be an ideal of finite codimension in \({\mathcal O}_n\). The toroidal embedding associated to the Newton polyhedron of \(I\) is constructed. It is shown that the integral closure of ideals with Newton non-degenerate polyhedron is determined precisely by the set of elements which are in the Newton polyhedron.

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
13B22 Integral closure of commutative rings and ideals
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