This is not the case in general. There are examples already with M = I such that reg(I) > 2 reg(I), see Sturmfels [15] and Terai [16]. On the other hand, Chandler [5] and Geramita, Gimigliano and Pitteloud [11] have shown that reg(I) ≤ k reg(I) holds for ideals with dimR/I ≤ 1. In general one has that reg(I) is asymptotically a linear function of k, see [14, 8]. If one takes I = m and M any gra...

We establish bounds for the Castelnuovo-Mumford regularity of a finitely generated graded module and its symmetric powers in terms of the degrees of the generators of the module and the degrees of their relations. We extend to modules (and improve) the known bounds for homogenous ideal in a polynomial ring established by Galligo, Guisti, Caviglia and Sbarra.

The Castelnuovo-Mumford regularity r of a variety V ⊆ Pn C is an upper bound for the degrees of the hypersurfaces necessary to cut out V . In this note we give a bound for r when V is left invariant by a vector field on

D. J. Benson conjectures that the Castelnuovo-Mumford regularity of the cohomology ring of a finite group is always zero. More generally he conjectures that there is always a very strongly quasi-regular system of parameters. Computer calculations show that the second conjecture holds for all groups of order less than 256.

We consider the possibility of characterizing Buchsbaum and some special generalized Cohen-Macaulay rings by systems of parameters having certain properties of regular sequences. As an application, we give a bound on Castelnuovo-Mumford regularity of so-called (k, d)-Buchsbaum graded Kalgebras.

Citation: Iudici A, Faccio E and Castelnuovo G (2017) Commentary: Preliminary evaluation of an analog procedure to assess acceptability of intimate partner violence against women: the Partner Violence Acceptability Movie Task. Front. Psychol. 8:1766. doi: 10.3389/fpsyg.2017.01766 Commentary: Preliminary evaluation of an analog procedure to assess acceptability of intimate partner violence again...

We show that the Eisenbud-Goto conjecture holds for seminormal simplicial affine semigroup rings. Moreover we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the normal case. Finally we compute explicitly the regularity of full Veronese rings.

We study the equations defining a projective embedding of a toric variety X using multigraded Castelnuovo-Mumford regularity. Consider globally generated line bundles B1, . . . , Bl and an ample line bundle L := B ⊗m1 1 ⊗ B2 2 ⊗ · · · ⊗ Bl l on X . This article gives sufficient conditions on mi ∈ N to guarantee that the homogeneous ideal I of X in P := P (

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains bounds for the Castelnuovo-Mumford regularity of the Rees algebra and for the Artin-Rees numbers.