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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
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