Castelnuovo–Mumford Regularity and Powers

Winfried Bruns (), Aldo Conca () and Matteo Varbaro ()
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Winfried Bruns: Institut für Mathematik, Universität Osnabrück
Aldo Conca: Universitá di Genova, Dipartimento di Matematica
Matteo Varbaro: Universitá di Genova, Dipartimento di Matematica

A chapter in Commutative Algebra, 2021, pp 147-158 from Springer

Abstract: 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 rings R = ⊕ i ∈ ℕ R i $$R=\bigoplus _{i\in {\mathbb N}} R_i$$ over general base rings R0. 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 Iv 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 proof of a result proved by the authors in “Maximal minors and linear powers”.

Date: 2021
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DOI: 10.1007/978-3-030-89694-2_4

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