A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves

Shijie Shang

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arXiv · 2205.06289

A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves

Shijie Shang

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Abstract

We show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety $X\subseteq\mathbb{P}^r$ is sharp exactly for complete intersections, provided the variety $X$ is cut out scheme-theoretically by several hypersurfaces in $\mathbb{P}^r$. This generalizes a result of Bertram-Ein-Lazarsfeld.

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Shijie Shang. 2022-05-12. A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves. https://arxiv.org/abs/2205.06289

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