Stability of associated primes and equality of ordinary and symbolic powers of ideals

1999 ◽  
Vol 27 (7) ◽  
pp. 3221-3231 ◽  
Author(s):  
Susan Morey
Keyword(s):  
Associated Primes ◽  
Powers Of Ideals ◽  
Symbolic Powers

scholarly journals Limit behavior of the rational powers of monomial ideals

2021 ◽  
Author(s):  
James Lewis
Keyword(s):  
Local Cohomology ◽  
Integral Closure ◽  
Monomial Ideals ◽  
Limit Behavior ◽  
Associated Primes ◽  
Powers Of Ideals ◽  
Symbolic Powers ◽  
Local Cohomology Modules ◽  
Cohomology Modules

We investigate the rational powers of ideals. We find that in the case of monomial ideals, the canonical indexing leads to a characterization of the rational powers yielding that symbolic powers of squarefree monomial ideals are indeed rational powers themselves. Using the connection with symbolic powers techniques, we use splittings to show the convergence of depths and normalized Castelnuovo–Mumford regularities. We show the convergence of Stanley depths for rational powers, and as a consequence of this, we show the before-now unknown convergence of Stanley depths of integral closure powers. Additionally, we show the finiteness of asymptotic associated primes, and we find that the normalized lengths of local cohomology modules converge for rational powers, and hence for symbolic powers of squarefree monomial ideals.

scholarly journals Fine behavior of symbolic powers of ideals

2007 ◽  
Vol 51 (1) ◽  
pp. 171-183 ◽  
Author(s):  
Melvin Hochster ◽  
Craig Huneke
Keyword(s):  
Powers Of Ideals ◽  
Symbolic Powers

scholarly journals On the equality of ordinary and symbolic powers of ideals

2012 ◽  
Vol 4 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Aline Hosry ◽  
Youngsu Kim ◽  
Javid Validashti
Keyword(s):  
Powers Of Ideals ◽  
Symbolic Powers

scholarly journals Comparing powers and symbolic powers of ideals

2010 ◽  
Vol 19 (3) ◽  
pp. 399-417 ◽  
Author(s):  
Cristiano Bocci ◽  
Brian Harbourne
Keyword(s):  
Powers Of Ideals ◽  
Symbolic Powers

Associated Primes of Powers of Ideals

2020 ◽  
pp. 3-11
Author(s):  
Enrico Carlini ◽  
Huy Tài Hà ◽  
Brian Harbourne ◽  
Adam Van Tuyl
Keyword(s):  
Associated Primes ◽  
Powers Of Ideals

scholarly journals Expected resurgences and symbolic powers of ideals

2020 ◽  
Vol 102 (2) ◽  
pp. 453-469
Author(s):  
Eloísa Grifo ◽  
Craig Huneke ◽  
Vivek Mukundan
Keyword(s):  
Powers Of Ideals ◽  
Symbolic Powers

scholarly journals Symbolic Powers of Ideals Defining F-pure and Strongly F-regular Rings

2017 ◽  
Vol 2019 (10) ◽  
pp. 2999-3014 ◽  
Author(s):  
Eloísa Grifo ◽  
Craig Huneke
Keyword(s):  
Regular Ring ◽  
Radical Ideal ◽  
Containment Problem ◽  
Powers Of Ideals ◽  
Symbolic Powers ◽  
Regular Rings

Abstract Given a radical ideal $I$ in a regular ring $R$, the Containment Problem of symbolic and ordinary powers of $I$ consists of determining when the containment $I^{(a)} \subseteq I^b$ holds. By work of Ein–Lazersfeld–Smith, Hochster–Huneke and Ma–Schwede, there is a uniform answer to this question, but the resulting containments are not necessarily best possible. We show that a conjecture of Harbourne holds when $R/I$ is F-pure, and prove tighter containments in the case when $R/I$ is strongly F-regular.

scholarly journals Symbolic Powers of Ideals

2018 ◽  
pp. 387-432 ◽  
Author(s):  
Hailong Dao ◽  
Alessandro De Stefani ◽  
Eloísa Grifo ◽  
Craig Huneke ◽  
Luis Núñez-Betancourt
Keyword(s):  
Powers Of Ideals ◽  
Symbolic Powers
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