In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree . We define some operations on the clutters associated to such ideals and prove that the regularity is preserved under these operations. We apply these operations to introduce some classes of ideals with linear resolutions and also show that any clutter corresponding to a triangulation of the sphere does not have linear resolution while any proper subclutter of it has a linear resolution.
Dans cet article nous étudions la régularité de Castelnuovo-Mumford des idéaux engendrés par des monômes libres de carré et de degré trois. Nous définissons des opérations sur l’ensemble des clutters associés à ces idéaux et démontrons que la régularité de Castelnuovo-Mumford est conservée par ces opérations. Ces opérations nous permettent d’introduire certaines classes d’idéaux ayant une résolution linéaire. En particulier nous démontrons qu’aucun clutter correspondant à une triangulation de la sphère a une résolution linéaire, mais par contre que tout subclutter propre a une résolution linéaire.
@article{AFST_2014_6_23_4_877_0,
author = {Marcel Morales and Abbas Nasrollah Nejad and Ali Akbar Yazdan Pour and Rashid Zaare-Nahandi},
title = {Monomial ideals with 3-linear resolutions},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {877--891},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {4},
year = {2014},
doi = {10.5802/afst.1428},
mrnumber = {3270427},
zbl = {06374892},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1428/}
}
TY - JOUR AU - Marcel Morales AU - Abbas Nasrollah Nejad AU - Ali Akbar Yazdan Pour AU - Rashid Zaare-Nahandi TI - Monomial ideals with 3-linear resolutions JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 877 EP - 891 VL - 23 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1428/ DO - 10.5802/afst.1428 LA - en ID - AFST_2014_6_23_4_877_0 ER -
%0 Journal Article %A Marcel Morales %A Abbas Nasrollah Nejad %A Ali Akbar Yazdan Pour %A Rashid Zaare-Nahandi %T Monomial ideals with 3-linear resolutions %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 877-891 %V 23 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1428/ %R 10.5802/afst.1428 %G en %F AFST_2014_6_23_4_877_0
Marcel Morales; Abbas Nasrollah Nejad; Ali Akbar Yazdan Pour; Rashid Zaare-Nahandi. Monomial ideals with 3-linear resolutions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 4, pp. 877-891. doi : 10.5802/afst.1428. https://afst.centre-mersenne.org/articles/10.5802/afst.1428/
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