Related papers: Mapping resolutions of length three I
Let $M$ be a perfect module of projective dimension 3 in a Gorenstein, local or graded ring $R$. We denote by $\FF$ the minimal free resolution of $M$. Using the generic ring associated to the format of $\FF$ we define higher structure…
Recent work on generic free resolutions of length 3 attaches to every resolution a graph and suggests that resolutions whose associated graph is a Dynkin diagram are distinguished. We conjecture that in a regular local ring, every grade 3…
Following an overview of the relevant theory, we construct several explicit examples of height-3 K3 spectra.
Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking…
The paper deals with recursive constructions for simple 3-designs based on other 3-designs having $(1, \sigma)$-resolution. The concept of $(1, \sigma)$-resolution may be viewed as a generalization of the parallelism for designs. We show…
In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
In previous work, we determined the metric dimension for a direct product of three isomorphic complete graphs. Turning to the case where the complete graphs may have different orders, there are three families we refer to as the upper,…
A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a differential graded algebra structure, based on which one can classify local rings of embedding…
In this paper we study resolutions which arise as iterated mapping cones.
This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special…
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…
A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd…
We define the notions of relative $e$-spectra, with respect to $E$-operators, relative closures, and relative generating sets. We study properties connected with relative $e$-spectra and relative generating sets.
Some constructions and bounds on the sizes of semiovals contained in the Hermitian curve are given. A construction of an infinite family of 2-blocking sets of the Hermitian curve is also presented.
In this paper I give an explicit construction of the generic ring R_{gen} for finite free resolutions of length 3. The corresponding problem for resolutions of length 2 was solved in 1970'ies by Hochster and Huneke. The key role is played…
The purpose of this paper is to verify a conjecture of Gross under mild hypothesis: all reduced, separated, and excellent schemes have the resolution property away from a closed subset of codimension at least three. Our technique uses…
We describe the resolution of singularities of a threefold which has minimal Picard number. We describe the relation between this minimal resolution and an arbitrary resolution of singularities.
In this paper we obtain some slight correction and generalization of the results of Ryabtseva on the generalized resolvents for isometric operators with a gap in their spectrum. Also, analogs of some McKelvey's results and a short proof of…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…