Betti numbers of symmetric shifted ideals

被引：14

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 37 条

[1] The Minimal Free Resolution of a Fat Star-Configuration in Pn
Ahn, Jeaman
Shin, Yong Su
[J]. ALGEBRA COLLOQUIUM, 2014, 21 (01) : 157 - 166
[2] THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY
Ahn, Jeaman
Shin, Yong Su
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (02) : 405 - 417
[3] [Anonymous], 2006, Graduate Texts in Mathematics
[4] [Anonymous], MACAULAY2 SOFTWARE S
[5] Finite generation of symmetric ideals
Aschenbrenner, Matthias
Hillar, Christopher J.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (11) : 5171 - 5192
[6] Bauer T, 2009, CONTEMP MATH, V496, P33
[7] COMPARING POWERS AND SYMBOLIC POWERS OF IDEALS
Bocci, Cristiano
Harbourne, Brian
[J]. JOURNAL OF ALGEBRAIC GEOMETRY, 2010, 19 (03) : 399 - 417
[8] Complete intersections on general hypersurfaces
Carlini, Enrico
Chiantini, Luca
Geramita, Anthony V.
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2008, 57 : 121 - 136
[9] Star configurations on generic hypersurfaces
Carlini, Enrico
Guardo, Elena
Van Tuyl, Adam
[J]. JOURNAL OF ALGEBRA, 2014, 407 : 1 - 20
[10] Cooper S. M., 2014, Springer Proc. Math. Stat, V76, P147

← 1 2 3 4 →