A corollary to the Evans-Griffith Syzygy theorem
A standard basis approach to syzygies of canonical curves.
About G-rings
In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if is a ring extension such that for some regular element of , then is a G-ring if and only if so is . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.
ACM sets of points in multiprojective space
Algebraic properties of edge ideals via combinatorial topology.
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
Betti numbers of some circulant graphs
Let be the greatest odd integer less than or equal to . In this paper we provide explicit formulae to compute -graded Betti numbers of the circulant graphs . We do this by showing that this graph is the product (or join) of the cycle by itself, and computing Betti numbers of . We also discuss whether such a graph (more generally, ) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or .
Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses
Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.
Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls.
The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls.
Castelnuovo-Mumford regularity of products of ideals.
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...
Castelnuovo's index of regularity and reduction numbers
Characterizations of some rings with -projective, -(FP)-injective and -flat modules
Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
Classifying Hilbert functions of fat point subschemes in P^2.
Cohen-Macaulay modifications of the vertex cover ideal of a graph
We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.
Combinatoric of syzygies for semigroup algebras.
We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.
Completeness conditions in certain Weyl complexes, combinatorics and parsimony.
Cremona transformations and syzygies.
Décomposition de la cohomologie cyclique bivariante des algèbres commutatives.
Deforming syzygies of liftable modules and generalised Knörrer functors
Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Divisors on Mg,g+1 and the minimal resolution conjecture for points on canonical curves