Betti numbers of symmetric shifted ideals

被引：13

作者：

Biermann, Jennifer ^{[1
]}

de Alba, Hernan ^{[2
]}

Galetto, Federico ^{[3
]}

Murai, Satoshi ^{[4
]}

Nagel, Uwe ^{[5
]}

O'Keefe, Augustine ^{[6
]}

Roemer, Tim ^{[7
]}

Seceleanu, Alexandra ^{[8
]}

机构：

[1] Hobart & William Smith Coll, Dept Math & Comp Sci, 300 Pulteney St, Geneva, NY 14456 USA

[2] Univ Autonoma Zacatecas, CONACyT UAZ, Unidad Acad Matemat, Calzada Solidaridad Entronque Paseo Bufa, Zacatecas 98000, Zac, Mexico

[3] Cleveland State Univ, Dept Math & Stat, Cleveland, OH 44115 USA

[4] Waseda Univ, Dept Math, Fac Educ, Shinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan

[5] Univ Kentucky, Dept Math, 715 Patterson Off Tower, Lexington, KY 40506 USA

[6] Connecticut Coll, Dept Math, 270 Mohegan Ave Pkwy, New London, CT 06320 USA

[7] Univ Osnabruck, Inst Math, D-49069 Osnabruck, Germany

[8] Univ Nebraska, Dept Math, 203 Avery Hall, Lincoln, NE 68588 USA

来源：

JOURNAL OF ALGEBRA | 2020年 / 560卷

关键词：

Betti numbers; Equivariant resolution; Linear quotients; Shifted ideal; Star configuration; Symbolic power; MINIMAL FREE RESOLUTION; STAR-CONFIGURATION;

D O I：

10.1016/j.jalgebra.2020.04.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations. (C) 2020 Elsevier Inc. All rights Inc. All rights reserved.

引用

页码：312 / 342

页数：31

共 50 条

[1] Betti numbers of monomial ideals and shifted skew shapes
Nagel, Uwe
Reiner, Victor
[J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 16 (02):
[2] BETTI NUMBERS OF PIECEWISELEX IDEALS
Jamroz, Christina
Sosa, Gabriel
[J]. JOURNAL OF COMMUTATIVE ALGEBRA, 2018, 10 (03) : 339 - 345
[3] Betti numbers of binomial ideals
de Alba, Hernan
Morales, Marcel
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 2017, 80 : 387 - 402
[4] Ideals with stable Betti numbers
Aramova, A
Herzog, J
Hibi, T
[J]. ADVANCES IN MATHEMATICS, 2000, 152 (01) : 72 - 77
[5] BETTI NUMBERS OF POWERS OF IDEALS
Failla, Gioia
La Barbiera, Monica
Stagliano, Paola L.
[J]. MATEMATICHE, 2008, 63 (02): : 191 - 195
[6] ON THE BETTI NUMBERS OF PERFECT IDEALS
VALLA, G
[J]. COMPOSITIO MATHEMATICA, 1994, 91 (03) : 305 - 319
[7] Betti numbers of determinantal ideals
Miro-Roig, Rosa M.
[J]. JOURNAL OF ALGEBRA, 2007, 318 (02) : 653 - 668
[8] BETTI NUMBERS OF PERFECT HOMOGENEOUS IDEALS
LORENZINI, A
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1989, 60 (03) : 273 - 288
[9] Betti Numbers of Transversal Monomial Ideals
Zaare-Nahandi, Rahim
[J]. ALGEBRA COLLOQUIUM, 2011, 18 : 925 - 936
[10] Multigraded Betti numbers of multipermutohedron ideals
Kumar, Ashok
Kumar, Chanchal
[J]. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2013, 28 (01) : 1 - 18

← 1 2 3 4 5 →