Date of Award

1995

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Patrick Gilmer

Abstract

Hilbert in his sixteenth problem asks us to study the topology of real algebraic varieties. There are many equalities, inequalities, and congruences associated to a real algebraic curve. Extremal properties have been derived for many of the inequalities. In 1980, V. A. Rokhlin derived two inequalities associated to a real algebraic curve. In this dissertation we use methods developed by P. Gilmer to rederive Rokhlin's inequalities. Using these methods we then derive an extremal property for one of the inequalities. Although this extremal property was not studied by Rokhlin, we also show that Rokhlin's ideas can be utilized to prove the extremal property.

Pages

77

Share

COinS