First off,I off, I wanted to commend you on this whole project,Ravi.Algebraic project, Ravi. Algebraic geometry and the theory of schemes is a notoriously difficult subject to internalize for any advanced student and it's clear you've given a lot of serious thought on how to make it more digestible. I've browsed the old version of the notes and found them very readable and highly thought out. I firmly support this project and hope it goes through many revisions and drafts,evolving drafts, evolving into a future classic. Algebraic geometry is a subject I haven't seriously begun broaching yet and I hope to use one of the newer versions when ready,
Secondly-I sympathize with your hesitancy to convert them into a book. What you might consider is creating an online text that will constantly be revised and will never be in "final" form. My old biochemistry professor Burton Tropp did this for many years and it worked out for him very well:The well: The first edition WAS published,but published, but all subsequent editions (and there was nearly a dozen before he retired last year) were online and subject to constant revision and improvement. I think this kind of format will work very well for you.
Thirdly -- history is so important in learning a new,conceptually difficult field. Some good historical notes would make the notes a lot more interesting to read no matter how good the exposition is. Students want to know how they came up with this crazy stuff-if stuff -- if you know how the original source authors came up with these concepts and why,it'll why, it'll make it a lot easier to not only internalize,but internalize, but also to form thier own opinions on the subject.
Fourthly-I
Fourthly -- I think inserting references and research assignments relying on significant papers,such papers, such as Grothendiek's original schemes paper-will paper -- will give your students some much needed research experience in a very active field. These are advanced students and the more such experience they get,the better off they'll be.
Lastly-I
Lastly -- I wanted to commend your humility and determination in asking other mathematicians and students for opinions and input on this project. It shows how committed you are to this project and experts should be chomping at the bit to give you thier feedback and opinions. I would,but would, but my lack of expertise precludes that. Hopefully those with much more knowledge then I will jump at the chance to assist you with this wonderful project.
Good luck with this exciting project and looking forward to future versions!!!
