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arXiv · 1904.07587

Depth functions of powers of homogeneous ideals

Huy Tai Ha·Hop Dang Nguyen·Ngo Viet Trung·Tran Nam Trung
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Abstract

We settle a conjecture of Herzog and Hibi, which states that the function depth $S/Q^n$, $n \ge 1$, where $Q$ is a homogeneous ideal in a polynomial ring $S$, can be any convergent numerical function. We also give a positive answer to a long-standing open question of Ratliff on the associated primes of powers of ideals.

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Huy Tai Ha, Hop Dang Nguyen, Ngo Viet Trung, Tran Nam Trung. 2019-04-16. Depth functions of powers of homogeneous ideals. https://doi.org/10.1090/proc/15083

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