Quadratic transform of complete ideals in regular local rings

D'Cruz, Clare

doi:10.1080/00927870008826852

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…Under the assumption that I is m-primary 2.14 is proved in [DC1,Lemma 3.3]. Further in [G, 2.4] it is proved that integrally closed ideals are m-full in a much more general context.…”

Section: M−full Contracted and Componentwise Linear Idealsmentioning

confidence: 99%

“…Special cases of Theorem 3.18 and Proposition 3.19 appear in [DC1]. In general, even for a normal ideal I the product mI need not be integrally closed, see [DC2,Example 7.1].…”

Section: It Follows Thatmentioning

confidence: 99%

“…In this direction we mention the work of Cutkosky [C, C1, C2, C3], Deligne [D], Huneke [H] and Lipman [L]. Several authors considered other related problems, as for instance the description of integrally closed ideals I such that Im is integrally closed as well, see [CGPU,DC1,DC2,EM,Ga,Ga1,HH].…”

Section: Introductionmentioning

confidence: 99%

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Integrally closed and componentwise linear ideals

2009

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Abstract. In a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is CohenMacaulay. In higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do. We restrict our attention to 0-dimensional homogeneous ideals in polynomial rings R of arbitrary dimension. We identify a class of integrally closed ideals, the Goto-class G * , which is closed under product and it has a suitable unique factorization property. Ideals in G * have a Cohen-Macaulay associated graded ring if either they are monomial or dim R ≤ 3. Our approach is based on the study of the relationship between the notions of integrally closed, contracted, full and componentwise linear ideals.

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“…Under the assumption that I is m-primary 2.14 is proved in [DC1,Lemma 3.3]. Further in [G, 2.4] it is proved that integrally closed ideals are m-full in a much more general context.…”

Section: M−full Contracted and Componentwise Linear Idealsmentioning

confidence: 99%

“…Special cases of Theorem 3.18 and Proposition 3.19 appear in [DC1]. In general, even for a normal ideal I the product mI need not be integrally closed, see [DC2,Example 7.1].…”

Section: It Follows Thatmentioning

confidence: 99%