TY - JOUR
T1 - Powers of principal Q-Borel ideals
AU - Camps-Moreno, Eduardo
AU - Kohne, Craig
AU - Sarmiento, Eliseo
AU - van Tuyl, Adam
N1 - Publisher Copyright:
© Canadian Mathematical Society 2020
PY - 2021
Y1 - 2021
N2 - Fix a poset Q on {x1, . . ., xn}. A Q-Borel monomial ideal I ⊆ K[x1, . . ., xn] is a monomial ideal whose monomials are closed under the Borel-like moves induced by Q. A monomial ideal I is a principal Q-Borel ideal, denoted I = Q(m), if there is a monomial m such that all the minimal generators of I can be obtained via Q-Borel moves from m. In this paper we study powers of principal Q-Borel ideals. Among our results, we show that all powers of Q(m) agree with their symbolic powers, and that the ideal Q(m) satisfies the persistence property for associated primes. We also compute the analytic spread of Q(m) in terms of the poset Q.
AB - Fix a poset Q on {x1, . . ., xn}. A Q-Borel monomial ideal I ⊆ K[x1, . . ., xn] is a monomial ideal whose monomials are closed under the Borel-like moves induced by Q. A monomial ideal I is a principal Q-Borel ideal, denoted I = Q(m), if there is a monomial m such that all the minimal generators of I can be obtained via Q-Borel moves from m. In this paper we study powers of principal Q-Borel ideals. Among our results, we show that all powers of Q(m) agree with their symbolic powers, and that the ideal Q(m) satisfies the persistence property for associated primes. We also compute the analytic spread of Q(m) in terms of the poset Q.
KW - Analytic spread
KW - Monomial ideals
KW - Persistence of primes
KW - Q-Borel
KW - Symbolic powers
UR - http://www.scopus.com/inward/record.url?scp=85113461879&partnerID=8YFLogxK
U2 - 10.4153/S0008439521000606
DO - 10.4153/S0008439521000606
M3 - Artículo
AN - SCOPUS:85113461879
SN - 0008-4395
VL - 65
SP - 633
EP - 652
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
IS - 3
ER -