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

2006/03/09 by Clare D’Cruz, Clare D'Cruz, D'Cruz, Clare
Computer Science · Mathematics · #13B22 #14E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13B22 #msc:14E15

paper · pdf · doi:10.48550/arxiv.math/0603211

23 pages. to appear in Journal of Algebra

arxiv created 2006/03/09 · openalex publication_date 2006/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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