Algebraic geometry is one of the subjects I’m most interested in, as might be inferred from many of my posts on this blog. I’ve discussed the idea of what algebraic geometry is all about, and hopefully for the readers of this blog this will suffice as motivation and introduction to this beautiful and grand subject whose developments have become a central ingredient to the story of modern mathematics, following the lead of one of the most influential mathematicians in modern times, Alexander Grothendieck.
The subject of algebraic geometry is vast, and many ideas are pretty abstract. On top of that, as I myself am still learning the subject, it might not be a very good idea for me to try and take on the subject, even just the basic aspects of it, in its entirety. One of my goals has been to present modern mathematics (and physics) to readers in a more accessible way, “bridging” perhaps the gap between the subject as taught in a university, and a layperson or a beginner who might not have had the access to more formal education in the subject. For this reason I have tried to make this blog as self-contained as possible, although I always provide references for those who want to follow-up on the introductory discussions made on the blog.
However, this goal would perhaps be too ambitious for me, or at least too inconvenient; it is also my goal (in fact my primary goal) to make this blog a sort of repository of notes that I make while studying, and I cannot accomplish this goal if I am bogged down too much in the exposition of the basics.
With all that said, there is actually a blog which has accomplished this ambitious goal of presenting algebraic geometry “from the beginning”. I therefore present the series AG from the Beginning at the blog Rigorous Trivialities, written mostly by Charles Siegel with contributions from Matt DeLand. My experience writing on my own blog has made me appreciate how much of an effort is put into a series like this, and as I continue to study I continue to read the posts to help with my own understanding. In fact, along with the blog This Week’s Finds in Mathematical Physics by John Baez (which goes back all the way to 1993), it was one of the blogs I looked up to for inspiration when starting this blog. From there I got the idea of trying to make things as self-contained as possible, but as I have said above with certain things I seem to have reached my limit, and with the existence of such a project, another attempt would perhaps be redundant.
As to the content of this blog, things will mostly remain the same, but I’ll take some of the load off my shoulders by simply linking to this series in my posts. This will allow me to not get bogged down too much in exposition, as I have said earlier, and I can take on certain subjects with much more freedom. Also, things are poised to get busier for me in the coming weeks, and I want to keep writing on this blog, so I think I could do with less mental pressure trying to discuss an entire subject in logical order (this, especially, has not historically been my strong suit). With some (but not all) of the subjects I have already discussed on this blog I am quite confident that I have already provided a reasonable amount of motivation and introduction for the reader; perhaps I can now also do more of what the tagline of the blog says, “ramblings” on math and physics (and stuff).