Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinitely many orbifolds on P uniformized by the complex 2-ball B2 and some orbifolds over K3 surfaces uniformized by B2. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which P is uniformized by the product of 1-balls B1× B1.

Given a basic K-coalgebra C, we study the left Gabriel-valued quiver (CQ,Cd) of C by means of irreduciblemorphisms between indecomposable injective leftC-comodules and by means of the powers rad of the radical rad of the category C-inj of the socle-finite injective left C-comodules. Connections between the valued quiver (CQ,C d) of C and the valued quiver (CQ,Cd) of a colocalization coalgebra q...

The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector bundles over algebraic curves via his celebrated GIT machinery. Later, in early 80’s Atiyah and Bott found an infinite dimensional symplectic quotient description of this moduli space. Since then, we...

In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...

This short, expository note proves existence of the maximal quotient of a variety by free rational curves. 1. Definition of a maximal free rational quotient Definition 1.1. Let V be a Deligne-Mumford stack over a field k, and denote the smooth locus by V sm ⊂ V . A 1-morphism f : Pk → V sm is a free rational curve to V if fTV is generated by global sections and has positive degree. Let S be an ...

The ElGamal encryption scheme is described in the setting of any finite cyclic group G. Among the groups of most interest in cryptography are the multiplicative group Z of the ring of integers modulo a prime p, and the multiplicative groups F of finite fields of characteristic two. The later requires finding irreducible polynomials h(x) and constructing the quotient ring . El-Kassar et al. modi...

Abstract For an irreducible and nonpositive matrix, we present the concepts of Perron complement matrix generalized matrix. An inequality that relates matrices inverse N 0 -matrices is derived. In addition, obtain quotient formula based on for Schur complements.

One of the basic problems in arithmetic mirror symmetry is to compare the number of rational points on a mirror pair of Calabi-Yau varieties. At present, no general algebraic geometric definition is known for a mirror pair. But an important class of mirror pairs comes from certain quotient construction. In this paper, we study the congruence relation for the number of rational points on a quoti...

Let R be an integral domain and let Q denote the quotient field of R. We investigate the structure of R-submodules of Q that are Q-irreducible, or completely Q-irreducible. One of our goals is to describe the integral domains that admit a completely Q-irreducible ideal, or a nonzero Q-irreducible ideal. If R has a nonzero finitely generated Q-irreducible ideal, then R is quasilocal. If R is int...

We study the polynomial representation of the rational Cherednik algebra of type An−1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic p analogues...