An immediate generalization of the classical McKay correspondence for Gorenstein quotient spaces C/G in dimensions r ≥ 4 would primarily demand the existence of projective, crepant, full desingularizations. Since this is not always possible, it is natural to ask about special classes of such quotient spaces which would satisfy the above property. In this paper we give explicit necessary and suf...

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of “quotients” under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving Mumford’s geometric invariant theory (GIT). We concentrate on actions of unipotent groups H, and define sets of stable points X and semista...

In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T0 reflection. Finally, we introduce some c...

In this paper,we introduce a new verifiable multi-use multi-secretsharing scheme based on automata and one-way hash function. The scheme has theadversary fuzzy structure and satisfy the following properties:1) The dealer can change the participants and the adversary fuzzy structure without refreshing any participants' real-shadow. 2) The scheme is based on the inversion of weakly invertible fin...

Abstract Stateless ordered restart-delete automata (stl-ORD-automata) are studied. These obtained from the stateless restarting (stl-ORWW-automata) by introducing an additional operation, which, based on surrounding context, deletes a single letter. While stl-ORWW-automata accept regular languages, we show that swift stl-ORD-automata yield characterization for class of context-free languages. H...