Hyperovals in Desarguesian Planes: An Electronic Update

Welcome to my Hyperovals web page. This page is an experimental attempt to more fully utilize the capabilities of the World Wide Web as a mathematical research tool. At present the page just contains an electronic survey paper and some auxillary files, but future plans are to expand the page to include more details on individual hyperovals and their characteristics.

The electronic paper is an updating of two earlier surveys ([Ch88] and [Ch96]) concerned with the hyperovals in Desarguesian planes of even order, however, we should mention a more comprehensive print survey by Korchmáros [Ko91] which deals with ovals and related structures in arbitrary projective planes. Much of the work reported here is too recent to have been included in [Ko91]. A comment made in [Ch96];

``Progress in this area has been so rapid during the past two years that it is most likely that this paper will be out of date before it is published, ...''
has turned out to be prophetically true. To avoid repetitions of this problem we have turned to this electronic format, hoping that its timely updating and accessibility will be of value to the mathematical community.

Navigation Aids

Besides the index bar above, to help navigate through the web site I have incorporated the following navigation buttons in the pages:
[next] Next Button
In a linearly ordered set of topics or pages, this moves to the next item in the order.

[last] Last Button
In a linearly ordered set of topics or pages, this moves to the previous item in the order.

[forward] Fast Forward Button
Moves to a forward reference of the topic.

[back] Back Button
Moves to a previous reference to the topic.

[more] More Button
Moves to an amplification of the topic.

[proof] Proof Button
Proofs are not included in the main stream of the pages, but when they are provided they can be accessed by this button.

Ordinary links in the page are to either definitions (also available in the glossary) or to references (also available in the bibliography). These will appear in the lower bar. (To regain the table of contents in the lower bar, click on Table of Contents in the upper bar.) If I have not provided the appropriate link at some point, you will have to rely on your browser's navigation abilities.

Besides these navigational tools, I have also included a search engine (search index above) which will search these pages for any subject you type in.

The natural place to start examining these pages is with the Table of Contents. [next]