相关论文: Spinor structures on free resolutions of codimensi…

In this article we study minimal free resolutions of Gorenstein ideals of codimension four, using methods coming from representation theory. We introduce families of higher structure maps associated with such resolution, defined similarly…

I describe the projective resolution of a codimension 4 Gorenstein ideal, aiming to extend Buchsbaum and Eisenbud's famous result in codimension 3. The main result is a structure theorem stating that the ideal is determined by its (k+1) x…

We study Gorenstein ideals of codimension $4$ derived from generic doublings of almost complete intersection perfect ideals of codimension $3$. We also investigate spinor coordinates of such Gorenstein ideals with $8$ and $9$ generators.…

In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. This family is likely to play a key role in classifying…

The famous structure theorem of Buchsbaum and Eisenbud gives a complete characterization of Gorenstein ideals of codimension 3 and their minimal free resolutions. We generalize the ideas of Buchsbaum and Eisenbud from Gorenstein ideals to…

Starting with a grade three perfect ideal $I \subset R$, we demonstrate how to produce the a self-dual resolution of length four using the resolution of the original ideal. This process is also reversible. The main case of interest is when…

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes…

The main achievement of this paper is to provide a structure theorem for Artinian, Gorenstein local rings with the property that the square of the maximal ideal is generated by two elements. The moduli problem for this class of local…

In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework…

Rosenfeld's geometric approach to spinors is considered, according to which the coordinates of spinors are represented by the coordinates of the plane generators of the maximal dimension of the absolutes of non-Euclidean spaces. As an…

We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and…

Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…

In the work some relations between three techniques, Hopf's bundle, Kustaanheimo-Stiefel's bundle, 3-space with spinor structure have been examined. The spinor space is viewed as a real space that is minimally (twice as much) extended in…

We give explicit generators for ideals of two classes of subspace arrangements embedded in certain reflection arrangements, generalizing results of Li-Li and Kleitman-Lovasz. We also give minimal generators for the ideals of arrangements…

A main ingredient for Kustin-Miller unprojection, as developed in (S. Papadakis and M. Reid, Kustin-Miller unprojection without complexes, math.AG/0011094), is the module Hom_R(I, \om_R), where R is a local Gorenstein ring and I a…

We construct two families of free resolutions that resolve the ideals of certain opposite Schubert varieties restricted to the big open cell. We conjecture that these examples have genericity properties translating to structure theorems for…

We investigate the existence of ideals $I$ in a one-dimensional Gorenstein local ring $R$ satisfying $\mathrm{Ext}^{1}_{R}(I,I)=0$.

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a…

This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known…

We define the Kodaira dimension for $3$-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the…