Monomial ideals with 3-linear resolutions

Marcel Morales; Abbas Nasrollah Nejad; Ali Akbar Yazdan Pour; Rashid Zaare-Nahandi

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 4, page 877-891
  • ISSN: 0240-2963

Abstract

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In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree 3 . 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.

How to cite

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Morales, Marcel, et al. "Monomial ideals with 3-linear resolutions." Annales de la faculté des sciences de Toulouse Mathématiques 23.4 (2014): 877-891. <http://eudml.org/doc/275357>.

@article{Morales2014,
abstract = {In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree $3$. 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.},
author = {Morales, Marcel, Nasrollah Nejad, Abbas, Akbar Yazdan Pour, Ali, Zaare-Nahandi, Rashid},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Castelnuovo-Mumford regularity; square free monomial ideals; clutter; linear resolutions},
language = {eng},
number = {4},
pages = {877-891},
publisher = {Université Paul Sabatier, Toulouse},
title = {Monomial ideals with 3-linear resolutions},
url = {http://eudml.org/doc/275357},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Morales, Marcel
AU - Nasrollah Nejad, Abbas
AU - Akbar Yazdan Pour, Ali
AU - Zaare-Nahandi, Rashid
TI - Monomial ideals with 3-linear resolutions
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 4
SP - 877
EP - 891
AB - In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree $3$. 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.
LA - eng
KW - Castelnuovo-Mumford regularity; square free monomial ideals; clutter; linear resolutions
UR - http://eudml.org/doc/275357
ER -

References

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  9. Morales (M.), Yazdan Pour (A.-A.), Zaare-Nahandi (R.).— The regularity of edge ideals of graphs. J. Pure Appl. Algebra 216, No. 12, p. 2714-2719 (2012). Zbl1316.13017MR2943752
  10. Decker (W.), Greuel (G.-M.), G. Pfister (G.), H. Schönemann (H.).— Singular 3-1-3 — A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2011). Zbl0902.14040
  11. Stanley (R.).— Combinatorics and Commutative Algebra, second ed., Progress in Mathematics, vol. 41, Birkhäuser Boston Inc., Boston, MA, (1996). Zbl0838.13008MR1453579
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