Stability of depths of symbolic powers of Stanley-Reisner ideals

被引：20

作者：

Le Than Hoa ^{[1
]}

Kimura, Kyouko ^{[2
]}

Terai, Naoki ^{[3
]}

Tran Nam Trung ^{[1
]}

机构：

[1] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

[2] Shizuoka Univ, Fac Sci, Dept Math, Suruga Ku, 836 Ohya, Shizuoka 4228529, Japan

[3] Saga Univ, Fac Culture & Educ, Saga 8408502, Japan

来源：

JOURNAL OF ALGEBRA | 2017年 / 473卷

关键词：

Depth; Symbolic power; Stanley-Reisner ideal; Cover ideal; MONOMIAL IDEALS; PERSISTENCE; GRAPHS;

D O I：

10.1016/j.jalgebra.2016.10.036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a bound for n(0)(I) from which the depth function depth R/I-(n) of the quotient ring by symbolic powers of a squarefree monomial ideal I stabilizes. In the unmixed corlimension two case we show that depth R/I-(n) is a non increasing function of n and use this property to provide a sharp bound for n(0)(I). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：307 / 323

页数：17

共 21 条

[1] [Anonymous], 1993, CAMBRIDGE STUDIES AD
[2] [Anonymous], 1998, Theory of linear and integer programming
[3] ASYMPTOTIC NATURE OF THE ANALYTIC SPREAD
BRODMANN, M
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1979, 86 (JUL) : 35 - 39
[4] Koszulness, Krull dimension, and other properties of graph-related algebras
Constantinescu, Alexandru
Varbaro, Matteo
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2011, 34 (03) : 375 - 400
[5] Bounds on the regularity and projective dimension of ideals associated to graphs
Dao, Hailong
Huneke, Craig
Schweig, Jay
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2013, 38 (01) : 37 - 55
[6] Giang D. H., 2010, ACTA MATH VIETNAM, V35, P229, DOI DOI 10.1007/s40306-014-0060-5
[7] On the radical of a monomial ideal
Herzog, J
Takayama, Y
Terai, N
[J]. ARCHIV DER MATHEMATIK, 2005, 85 (05) : 397 - 408
[8] The depth of powers of an ideal
Herzog, J
Hibi, T
[J]. JOURNAL OF ALGEBRA, 2005, 291 (02) : 534 - 550
[9] Symbolic powers of monomial ideals and vertex cover algebras
Herzog, Juergen
Hibi, Takayuki
Trung, Ngo Viet
[J]. ADVANCES IN MATHEMATICS, 2007, 210 (01) : 304 - 322
[10] Persistence and stability properties of powers of ideals
Herzog, Juergen
Qureshi, Ayesha Asloob
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (03) : 530 - 542

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