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...

1. Introduction. A prime q is a common index divisor of the algebraic number field Kii q divides the quotient d(u>)/d for all integers cu of K, where d(u>) is the discriminant of w and d is the discriminant of the field. A necessary condition is that q be less than the degree of

We classify, up to isomorphism, maximal curves covered by the Hermit-ian curve H by a prime degree Galois covering. We also compute the genus of maximal curves obtained by the quotient of H by several automorphisms groups. Finally we discuss the value for the third largest genus that a maximal curve can have.

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .

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...

Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F ) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F )]-modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on automatic realizability.

Let K be a complete discrete valuation field with ring of integers OK and algebraically closed residue field k of characteristic p > 0. Let X/K be a smooth proper geometrically connected curve of genus g > 0, withX(K) 6= ∅ if g = 1. Assume thatX/K does not have good reduction, and that it obtains good reduction over a Galois extension L/K of degree p. Let Y/OL be the smooth model of XL/L. Let H...