Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ ab(a− 1)(b− 1)/2 with the exception of the case a = b = 2, where the regularity is 4. Note that ab(a− 1)(b...

Article history: Received 7 October 2016 Received in revised form 16 January 2017 Available online xxxx Communicated by S. Iyengar To the memory of our friend Tony Geramita MSC: 13D02; 13D40 We give a simple proof for the fact that the Castelnuovo–Mumford regularity and related invariants of products of powers of ideals are asymptotically linear in the exponents, provided that each ideal is gen...

We characterize all pairs of graphs (G1, G2), for which the binomial edge ideal JG1,G2 has linear relations. We show that JG1,G2 has a linear resolution if and only if G1 and G2 are complete and one of them is just an edge. We also compute some of the graded Betti numbers of the binomial edge ideal of a pair of graphs with respect to some graphical terms. In particular, we show that for every p...

Here we define the concept of Qregularity for coherent sheaves on quadrics. In this setting we prove analogs of some classical properties. We compare the Qregularity of coherent sheaves on Qn ⊂ P n+1 with the Castelnuovo-Mumford regularity of their extension by zero in P. We also classify the coherent sheaves with Qregularity −∞. We use our notion of Qregularity in order to prove an extension o...

We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d − 1. This result allows to prove partial regularity results (i.e. closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary...

Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X . Given globally generated line bundles B1, . . . , Bl on X and m1, . . . , ml ∈ N, consider the line bundle L := B m1 1 ⊗ · · · ⊗ Bl l . We give conditions on the mi which guarantee that the ideal of X in P(H (X, L)∗) is generated by quadrics and the first p syzygies are line...

We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generated by the Hilbert functions of all modules, all modules with bounded a-invariant, and all modules with bounded Castelnuovo–Mumford regularity. The f...

For a smooth projective variety X ⊂ P embedded by the complete linear system, Property Np has been studied for a long time([5], [11], [12], [10] etc). On the other hand, Castelnuovo-Mumford regularity conjecture and related problems have been focused for a projective variety which is not necessarily linearly normal([2], [13], [15], [17], [20] etc). This paper aims to explain the influence of Pr...

We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the n-formality of these hyperplane arrangements. As an application, we are able to bou...