Mathematical correspondences

Alignment Correspondences

φ : R→̃ÔX,p with φ(I1, . . . , Ir) = (a1, . . . , ar)} and its closure C(I1, . . . , Ir) in the appropriate product of Hilbert schemes. If the ideals Ij are monomial, we will say that the space C(I1, . . . , Ir) is an alignment correspondenceswith interior U(I1, . . . , Ir). The significance of the Ij’s being monomial is that in this case we can show that the space U(I1, . . . , Ir) in most case...

Correspondences of Ribbon Categories

Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in...

On K3 Correspondences

We consider relationships between families of K3 surfaces, in the context of string theory. An important ingredient of string theory also of interest in algebraic geometry is T-duality. Donagi and Pantev [DP] have extended the original duality on genus one fibred K3 surfaces with a section to the case of any genus one fibration, via a Fourier-Mukai transform. We investigate possibilities of ext...

Modal Frame Correspondences Generalized

Equally Distributed Correspondences

The study of measurable and integrable selections from a correspondence (set-valued function) has been of interest for some time [e.g., see Aumann (1965), Hildenbrand (1974), etc.]. Here we take up the study of distributions of such selections. The motivation for doing this comes from Mathematical Economics [see Kannai (1970, section 7); the reader interested in the economic applications is ref...