In [6], Kontsevich and Zorich conjecture that the fundamental groups of strata of the moduli space of abelian differentials are commensurable with various mapping class groups. In this paper we consider a similar question for strata of quadratic differentials, and in particular we construct a quotient group of the fundamental group for a certain family of strata. We do so by mapping a stratum i...

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

We give an algorithm that, for a given value of the geometric genus $p_g,$ computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and system isolated base points. use it to show there are exactly two families such map degree $32$. also construct surface $q=1$ $24$. These $p_g=3$ point free system. discuss case $p_g=4$

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...

Let G be an algebraic torus acting on a smooth variety V . We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V . Let G be a reductive algebraic group acting on a smooth variety V . The cotangent bundle T V admits a canonical algebraic symplectic structure, and the induced action of G on T V is hamiltonian, that is, it admits ...

Let G be an algebraic torus acting on a smooth variety V . We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V . Let G be a reductive algebraic group acting on a smooth variety V . The cotangent bundle T V admits a canonical algebraic symplectic structure, and the induced action of G on T V is hamiltonian, that is, it admits ...