Claudia Polini, Bernd Ulrich, Wolmer V. Vasconcelos
We establish bounds for the coefficient $\bar{e}_1(I)$ of the Hilbert function of the integral closure filtration of equimultiple ideals. These values are shown to help control all algorithmic processes of normalization that make use of extensions satisfying the condition $S_2$ of Serre.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We generalize a Briançon-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\m)$ containing a field, and an ideal $I$ of $R$ with analytic spread $\ell$ and a minimal reduction $J$, we prove that for all $w \geq -1$, $ \bar{I^{\ell+w}} \subseteq J^{w+1} \mathfrak{a} (I,J),$ where $\mathfrak{a}(I,J)$ is the coefficient ideal of $I$ relative to $J$, i.e. the largest ideal $\mathfrak{b}$ such that $I\mathfrak{b}=J\mathfrak{b}$. Previously, this result was known only for $\m$-primary ideals.
We establish a generalization of the Briancon-Skoda theorem about integral closures of ideals for graded systems of ideals satisfying a certain geometric condition.
The Briançon-Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring $(R,\m)$, and an ideal $I$ of $R$ of analytic spread $\ell$ and height $g < \ell$, we improve on two theorems by Aberbach and Huneke. Let $J$ be a reduction of $I$. We first give results on when the integral closure of $I^\ell$ is contained in the product $J I_{\ell-1}$, where $I_{\ell-1}$ is the intersection of the primary components of $I$ of height $\leq \ell-1$. In the case that $R$ is also Gorenstein, we give results on when…
The Briancon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I\subset R and r\geq 1, the integral closure of I^{k+r-1} is contained in I^r. We compute the Briancon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.
The goal of this note is to survey some recent results on the Grauert-Riemenschneider multiplier ideal sheaves on any (reduced) complex space of pure dimension. In particular, we obtain the Briançon-Skoda number for any Noetherian ring of weakly holomorphic functions with weakly rational singularities (\emph{not} essentially of finite type over $\mathbb{C}$ and Cohen-Macaulay local rings), which will partially answer a question of Huneke.
We give a new elementary proof of the Briançon-Skoda theorem, which states that for an $m$-generated ideal $\mathfrak{a}$ in the ring of germs of analytic functions at $0\in \C^n$, the $ν$:th power of its integral closure is contained in $\mathfrak{a}$, where $ν= \min(m,n)$.
We present here an analogue of the Briançon-Skoda theorem for a germ of an analytic space $Z$ at 0, such that $O_{Z,0}$ is Cohen-Macaulay, but not necessarily reduced. More precisely, we find a sufficient condition for membership of a function in a power of an arbitrary ideal $a^l \subset O_{Z,0}$ in terms of size conditions of Noetherian differential operators applied to that function. This result generalizes a theorem by Huneke in the reduced case.
The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras
本文证明任何充分函子化的大Cohen-Macaulay代数指派所诱导的理想闭包运算都满足Briançon-Skoda型性质，并在混合特征下借助Bhatt的结果加强了Heitmann的定理。
The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings
本文证明了一个广义Briançon-Skoda型包含关系，并由此推出伪有理奇点（如正则环）和Du Bois奇点下的完整Briançon-Skoda包含，同时应用于证明有限维拟优秀环的一致Artin-Rees定理和一致Briançon-Skoda定理。
We show in this paper that the Briancon-Skoda theorem holds for all ideals in F-rational rings of positive prime characteristic, and also in rings with rational singularities which are of finite type over a field of characteristic 0. Moreover, in Gorenstein F-rational rings of characteristic p we show that in many cases the bound given in the Briancon-Skoda theorem may be improved by at least one.
The test ideal $τ(R)$ of a ring $R$ of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal $τ(\a^t)$ associated to a given ideal $\a$ with rational exponent $t \ge 0$. We first prove a key lemma of this paper, which gives a characterization of the ideal $τ(\a^t)$. As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal $τ(R)$. Moreover, we prove an analog of so-called Skoda's theorem, which is formulated algebraically via adjoint ideals by Lipm…
This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings is studied, and criteria are given for when the $s$-closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak $s$-closure to equal to the $s$-closure. A generalization of the Briancon-Skoda theorem is given which compares any two different $s$-closures applied to powers o…
We introduce a new variant of tight closure associated to any fixed ideal $\a$, which we call $\a$-tight closure, and study various properties thereof. In our theory, the annihilator ideal $τ(\a)$ of all $\a$-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal $τ(\a)$ and the multiplier ideal associated to $\a$ (or, the adjoint of $\a$ in Lipman's sense) in normal $\Q$-Gorenstein rings reduced from characteristic zero to characteristic $p \gg 0$. Also, in fixed prim…
We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers of ideals in regular rings. The author recently proved these bounds in mixed characteristic using various versions of perfectoid/big Cohen-Macaulay test ideals, with special cases obtained earlier by Ma and Schwede. In mixed characteristic, we instead use Heitmann's full extended plus (epf) closure, Jiang's weak epf (wepf) closure, and R.G.'s results on closure operations that induce big Cohen-Macaulay algebras. Our strategy also applies to any Dietz closure satisfying R.G.'s algebra axiom and a Brianço…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。