Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
COMBINATORIAL PROPERTIES OF ALGEBRAIC SETS
Abstract
In this thesis, we investigate those properties of an algebraic set that are determined by its partially ordered set of subvarieties. These properties are called the combinatorial properties of the algebraic set. We say that two algebraic sets are combinatorially equivalent (or homeomorphic) if their partially ordered set of subvarieties are isomorphic. In section one of this thesis we will classify, up to combinatorial equivalence, all affine surfaces over the algebraic closure of a finite field. In section two we discuss the combinatorial structure of projective and quasi-projective surfaces. We show, by example, that the combinatorial structure is more varied than in the affine case. Although the results are inconclusive, we prove that through each point P on a non-singular plane projective curve C over the algebraic closure of a finite field there is another curve D that meets C exactly at P. In the last section of this paper we discuss the Picard group of an affine ring. In particular, we have found necessary and sufficient conditions for a one-dimensional affine ring over any field to have torsion Picard group. For affine rings of larger dimensions, we have some partial results.
Subject Area
Mathematics
Recommended Citation
KRAUTER, WILLIAM WARREN, "COMBINATORIAL PROPERTIES OF ALGEBRAIC SETS" (1980). ETD collection for University of Nebraska-Lincoln. AAI8110574.
https://digitalcommons.unl.edu/dissertations/AAI8110574