The purpose of this paper is to establish a Castelnuovo-Mumford regularity bound for threefolds with mild singularities. Let X be non-degenerate normal projective threefold in Pr degree d and codimension e. We prove that if has rational singularities, then reg(X)≤d−e+2. Our very close sharp conjectured by Eisenbud-Goto. When e=2 Cohen-Macaulay Du Bois we obtain the reg(X)≤d−1, also classify ext...

We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30

We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free-boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford-Shah functional.

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.

Abstract We provide a homological construction of unitary simple modules Cherednik and Hecke algebras type A via BGG resolutions, solving conjecture Berkesch–Griffeth–Sam. vastly generalize the its solution to cyclotomic over arbitrary ground fields, calculate Betti numbers Castelnuovo–Mumford regularity certain symmetric linear subspace arrangements.