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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.

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