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arXiv · 2309.15083

Fluctuations in depth and associated primes of powers of ideals

Roswitha Rissner·Irena Swanson
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Abstract

We count the numbers of associated primes of powers of ideals as defined by Bandari, Hibi, and Herzog in 2014. We generalize those ideals to monomial ideals $\operatorname{BHH}(m,r,s)$ for $r \ge 2$, $m$, $s \ge 1$; we establish partially the associated primes of powers of these ideals, and we establish completely the depth function of quotients by powers of these ideals: the depth function is periodic of period $r$ repeated $m$ times on the initial interval before settling to a constant value. The number of needed variables for these depth functions are lower than those from general constructions by H\`{a}, Nguyen, Trung, and Trung (2021).

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Roswitha Rissner, Irena Swanson. 2023-09-26. Fluctuations in depth and associated primes of powers of ideals. https://doi.org/10.4310/arkiv.2024.v62.n1.a10

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