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arXiv · 2107.14734

Castelnuovo-Mumford regularity and powers

Winfried Bruns·Aldo Conca·Matteo Varbaro
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Abstract

This note has two goals. The first is to give a short and self contained introduction to the Castelnuovo-Mumford regularity for standard graded ring $R$ over a general base ring. The second is to present a simple and concise proof of a classical result due to Cutkosky, Herzog and Trung and, independently, to Kodiyalam asserting that the regularity of powers of an homogeneous ideal $I$ of $R$ is eventually a linear function in $v$. Finally we show how the flexibility of the definition of the Castelnuovo-Mumford regularity over general base rings can be used to give a simple characterization of the ideals whose powers have a linear resolution in terms of the regularity of the Rees ring.

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Winfried Bruns, Aldo Conca, Matteo Varbaro. 2021-07-30. Castelnuovo-Mumford regularity and powers. https://arxiv.org/abs/2107.14734

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