Castelnuovo–Mumford Regularity

For standard graded algebras over fields, Castelnuovo-Mumford regularity has become an indispensable invariant. Chapter 8 develops this notion from scratch, but in a more general version for standard graded algebras over Noetherian base rings. As in the classical case, regularity can be computed from local cohomology, minimal free resolutions and Koszul homology. In the given generality we prove the theorems on the regularity of powers and products of ideals. In the context of determinantal rings we are mainly interested in linear free resolutions of powers of ideals of maximal minors in the non-generic case, exemplified by ideals of rational normal scrolls.