1. Given a 3-dimensional Pappian projective space, it is well known that the Grassmannian which is representing its set of lines is a quadric (called the Pltcker quadric) in a 5-dimensional projective space. The link between the set of lines and the Pltcker quadric is the bijective Klein map g. Under g pencils of lines become lines of the Pltcker quadric. Cf. e.g. [5,287], [15,28], [16,13], [20...

in this paper, sufficient conditions for the existence ofcommon fixed points for a compatible pair of self maps of gregustype in the framework of convex metric spaces have been obtained.also, established the existence of common fixed points for a pair ofcompatible mappings of type (b) and consequently for compatiblemappings of type (a). the proved results generalize and extend someof the well k...

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

A notion of localized splitting is introduced as a further extension of the splitting notions for iterated monotone maps introduced earlier by Dubins and Freedman (1966) and more generally by Bhattacharya and Majumdar (1999). We will see that under quite general conditions, localized splitting theory is a natural extension of the Doeblin (1937) minorization theory, Harris (1956) recurrence theo...

We explore the relationship between limit linear series and fibers of Abel maps in the case of curves with two smooth components glued at a single node. To an r-dimensional limit linear series satisfying a certain exactness property (weaker than the refinedness property of Eisenbud and Harris) we associate a closed subscheme of the appropriate fiber of the Abel map. We then describe this closed...

In this paper, we discuss the theories of admissible covers (HarrisMumford) and limit linear series (Eisenbud-Harris), two techniques for using degenerations to study maps between curves. While the theories are superficially very similar, they have certain fundamental differences which we will also explore. 1. Motivational problems We begin by laying out a number of questions on curves which sh...

Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings. 0. Introduction. We study affine rings (i.e., rings finitely generated as algebras ov...