Characterizing the homogeneous variety F4(4)

The Homogeneous Coordinate Ring of a Toric Variety

This paper will introduce the homogeneous coordinate ring S of a toric variety X . The ring S is a polynomial ring with one variable for each one-dimensional cone in the fan ∆ determining X , and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of X (where n = dimX). Using this graded ring, we will show that X behaves like projective space ...

Murre’s Conjecture for a Rational Homogeneous Bundle over a Variety

In this paper, we investigate Murre’s conjectures on the structure of rational Chow groups for a rational homogeneous bundle Z → S over a smooth variety. Absolute Chow-Künneth projectors are exhibited for Z whenever S has a Chow–Künneth decomposition.

Characterizing and Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players

We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individ...

Characterizing sub-topical functions

In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

Characterizing bifurcations and chaos in multiwavelength lasers with intensity-dependent loss and saturable homogeneous gain