Integral closedness of $MI$ and the formula of Hoskin and Deligne for finitely supported complete ideals

Details Integral closedness of $MI$ and the formula of Hoskin and Deligne for finitely supported complete ideals Integral closedness of $MI$ and the formula of Hoskin and Deligne for finitely supported complete ideals

2006-03-09

arxiv.org/abs/math/0603211v1

Mathematics

Commutative Algebra

23 pages. to appear in Journal of Algebra

Scientific paper

In this paper we find a formula for the length of a finitely supported
complete ideal in terms of the order of the strict transform of the ideal. This
formula was known for complete ideals of height two in a two dimensional
regular local ring and was proved independently by Hoskin and Deligne. Several
consequences are deduced from this formula.

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