Geodesic
Powers of Principal Q-Borel ideals
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 633-652

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DOI

Fix a poset Q on $\{x_1,\ldots ,x_n\}$. A Q-Borel monomial ideal $I \subseteq \mathbb {K}[x_1,\ldots ,x_n]$ 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.
DOI : 10.4153/S0008439521000606
Mots-clés : monomial ideals, Q-Borel, symbolic powers, analytic spread, persistence of primes 
Camps-Moreno, Eduardo; Kohne, Craig; Sarmiento, Eliseo; Tuyl, Adam Van. Powers of Principal Q-Borel ideals. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 633-652. doi: 10.4153/S0008439521000606
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     title = {Powers of {Principal} {Q-Borel} ideals},
     journal = {Canadian mathematical bulletin},
     pages = {633--652},
     year = {2022},
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     number = {3},
     doi = {10.4153/S0008439521000606},
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