Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1, 4) as a generalization of Castelnuovo-Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the...

Abstract In this paper we study ideals of points lying on rational normal curves defined in projective plane and 3-space. We give an explicit formula for the value Castelnuovo–Mumford regularity their ordinary powers. Moreover, compare m -th symbolic powers such order to show whenever defect is non-zero.

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 topology of the lcm-lattice of edge ideals and derive upper bounds on the Castelnuovo-Mumford regularity of the ideals. In this context it is natural to restrict to the family of graphs with no induced 4-cycle in their complement. Using the above method we obtain sharp upper bounds on the regularity when the complement is a chordal graph, or a cycle, or when the primal graph is cla...