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

英文摘要：

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.