2021/07/30 by Bruns, Winfried, Conca, Aldo, Varbaro, Matteo
#13D02 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.14734
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.