Let G → GL(V) will be a finite-dimensional linear representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions: (i) Is the Luna stratification of X intrinsic? That is, ...

Let X be a projective normal toric variety and T0 a rank one subtorus of the defining torus of X. We show that the normalization of the Chow quotient X//T0, in the sense of Kapranov-Sturmfels-Zelevinsky, coarsely represents the moduli space of stable log maps to X with discrete data given by T0 ⊂ X.

This paper takes a new look at some old spaces. The old spaces are the moduli spaces of complete collineations, introduced and explored by many of the leading lights of 19th-century algebraic geometry, such as Chasles, Schubert, Hirst, and Giambelli. They are roughly compactifications of the spaces of linear maps of a fixed rank between two fixed vector spaces, in which the boundary added is a ...

We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

Darwinian evolution, which is characterized in terms of particular macroscopic behavior that emerges from microscopic organismic interaction, considers populations as units of evolutionary change. We formalize these concepts in evolutionary computation by developing notion of quotient evolutionary space(Q.E.S). We map set of all finite populations to a set of macroscopic properties of populatio...

The quotient digit selection in the SRT division algorithm is based on a few most significant bits of the remainder and divisor, where the remainder is usually represented in a redundant representation. The number of leading bits needed depends on the quotient radix and digit set, and is usually found by an extensive search, to assure that the next quotient digit can be chosen as valid for all ...

In classical covering space theory, a covering map induces an injection of fundamental groups. This note reveals a dual property for quotient maps having connected fibers, with applications to orbit spaces of smooth vector fields and leaf spaces in general.

A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of derivative this map reflect geometry product. We identify two classes extremal products: those that maximize difference between derivative, minimize it. Both turn out have same algebraic structure, being quotient hypergeometric polynomials.

This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley graphs (normal, bi-normal, and corefree), and analysing several operations of Cayley graphs (core quotient, normal quotient, and imprimitive quotient). It provides methods for constructing and characterising various c...