TY - JOUR
T1 - Regularity bounds for Koszul cycles
AU - Conca, Aldo
AU - Murai, Satoshi
N1 - Publisher Copyright:
© 2014 American Mathematical Society.
PY - 2015
Y1 - 2015
N2 - We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.
AB - We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.
KW - Castelnuovo-Mumford regularity
KW - Koszul cycles
KW - Koszul homology
UR - http://www.scopus.com/inward/record.url?scp=84919362769&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84919362769&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2014-12292-1
DO - 10.1090/S0002-9939-2014-12292-1
M3 - Article
AN - SCOPUS:84919362769
VL - 143
SP - 493
EP - 503
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 2
ER -