The behaviour of Castelnuovo-Mumford regularity under “geometric” transformations is not well understood. In this paper we are concerned with examples which will shed some light on certain questions concerning this behaviour. One simple question which was open (see e.g. [R]) is: May the regularity increase if we pass to the radical or remove embedded primes? By examples, we show that this happe...

We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not be Noetherian.

The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connections between two recent definitions of multigraded regularity with a view towards a better understanding of the multigraded Hilbert function of fat point schemes in P1 × · · · × Pk . MSC 2000: 13D02, ...