AGATHOS

Algebraic Geometry: A Total Hypertext Online System

AGATHOS is a hypertext-based, online system for learning algebraic geometry. I developed AGATHOS while teaching a year-long graduate class at the University of Maryland in College Park. Consequently, it makes some nontrivial assumptions about the backgrounds of its readers. The most important assumption is that the reader has completed a year-long graduate course in abstract algebra.

You can approach the subject in a variety of ways:

• As a linear text following the traditional order of presentation (definition, lemma, theorem, proof).
• Starting with a list of interesting examples of algebraic varieties.
• Starting with a list of important theorems in algebraic geometry.
• Starting with a list of key concepts in algebraic geometry.
• Starting with a list of exercises that can be solved using the ideas found elsewhere in these notes.

agathos

1. adj. good. (From the Greek, αγαθος.)

2. n. An online system for learning algebraic geometry.

Warning: The course in question occured during Fall Semester 1998. (You may find the selected quotations from that semester somewhat entertaining.) The front end looks really impressive, but a great many links are still empty. Not long after that, I started working on bioinformatics instead of algebraic geometry (I know; the connection between the two seems a bit tenuous), and have had little time to fill in the blanks.

Setup

When I first put these pages together back in 1998 and 1999, the HTML 4.0 specification was new, and none of the available browsers supported the named entities needed to include mathematical symbols. So, I resorted to a work-around that used the Symbol font, pointing out that I knew this would eventually have to be changed. In recent months, I have received several comments from readers about symbols not being displayed correctly, so I decided it was time to update the display instructions.

Sadly, the situtation is worse in 2005 than it was in 1999. Mozilla Firefox and the latest versions of Netscape (at least 7.0 and higher) have decided that it is "wrong" to use the Symbol font in the way that people have been using it for years. Instead, they have embraced the named entitites in the proposed HTML 4.0.1 standard. Current versions of Microsoft Internet Explorer (at least through version 6.0) fail to recognize the majority of the named entities. Even worse, instead of displaying the named entity (as they would if it were really unknown, like &unknownEntity;), which would allow most people to puzzle out the meaning, they replace many of them with useless blank boxes.

And so, providers of mathematical content on the web have to make a choice. Do they continue to use the Symbol font (via <FONT FACE="Symbol">) and support Internet Explorer, or do they switch to the HTML 4.0 named entities and support Netscape and Firefox? For these pages, I have decided that Firefox is the future, so mathematical symbols and Greek characters in the documents on this site are provided using the HTML4.0 character entities. As a result, most of the pages are difficult or impossible to interpret using Internet Explorer.

For readers unwilling to install the free version of Firefox as an alternate browser, the chapters are collected together as PDF files. In this way, at least, the situation has improved since 1999. Back then, I made TeX dvi files available (since most mathematicians had access to something that understood DVI files, even if their browser didn't quite know what to do with them). Improvements to pdftex and pdflatex have now made it easier to convert TeX source code into PDF outputs that look good. The disadvantage from the point of view of a truly hyperlinked text is that I haven't taken the time to make all teh hyperlinks work correctly in the PDF files, so that aspect of the text only works in the HTML version.

Comments on this web site should be addressed to the author: