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arXiv · 2610.26532

Saturation degree of powers of graded ideals

Le Tuan Hoa·Hop Dang Nguyen·Ngo Viet Trung
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Abstract

Let $I$ be a non-nilpotent graded ideal of a standard graded algebra over a Noetherian commutative ring. We show that the saturation degree sdeg $I^n$ is asymptotically a constant function or a linear function whose slope is one of the generating degrees of $I$. Furthermore, we give sufficient (and necessary) conditions for a numerical functions to be the function sdeg $I^n$ of an ideal $I$ generated by forms of the same degree. Our results may provide a better understanding of the initial behavior of the regularity function reg $I^n$.

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Le Tuan Hoa, Hop Dang Nguyen, Ngo Viet Trung. 2026-10-19. Saturation degree of powers of graded ideals. https://doi.org/10.1016/j.jpaa.2026.108392

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