Drinfeld’s relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection coho...

We study intersection homology with general perversities that assign integers to stratum components with none of the classical constraints of Goresky and MacPherson. We extend Goresky and MacPherson’s axiomatic treatment of Deligne sheaves, and use these to obtain Poincaré and Lefschetz duality results for these general perversities. We also produce versions of both the sheaf-theoretic and the ...

In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive alternative to category-theoretic (co)limits and show they have features similar to (pro-, in-)jections. Then we briefly discuss approaches to development of for...

In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.

In this paper we study duality for evaluation codes on intersections of d hypersurfaces with given d -dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of d = 2 it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and q...

In this paper, we develop a new approach to the discriminant of a complete intersection curve in the 3-dimensional projective space. By relying on the resultant theory, we first prove a new formula that allows us to define this discriminant without ambiguity and over any commutative ring, in particular in any characteristic. This formula also provides a new method for evaluating and computing t...

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideal...