On the symbolic powers of defining ideals of monomial curves associated to generalized arithmetic sequences

Let s , a , n , d be positive integers such that n ≥ 2 and GCD ( a , d ) = 1 . Let P denote the defining ideal of the monomial curve associated to the sequence a , sa + d , ... , sa + nd . In this survey, we investigate the symbolic powers of P. We first show that for each i > 1 the equality P (...

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Bibliographic Details
Published in:Communications in algebra 2024-09, Vol.52 (9), p.3970-3977
Main Author: Kien, Do Van
Format: Article
Language:English
Subjects:
Cohen-Macaulay ring
noetherian ring
numerical semigroup ring
symbolic power
symbolic Rees algebra
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Summary:Let s , a , n , d be positive integers such that n ≥ 2 and GCD ( a , d ) = 1 . Let P denote the defining ideal of the monomial curve associated to the sequence a , sa + d , ... , sa + nd . In this survey, we investigate the symbolic powers of P. We first show that for each i > 1 the equality P ( i ) = P i holds if and only if either n = 2 and a even or n = 3 , i = 2 and a ≡ 2   ( mod 3 ) . The finitely generated property of the symbolic Rees algebra R S ( P ) are also explored.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2337278