Algebraic varieties

The first post on this blog is titled “geometric intuition”, and discusses the geometry behind Noether’s normalization lemma. When I wrote it I didn’t yet understand all the pieces, as I was not very comfortable working with algebraic geometry. One year later, I’m still not comfortable, but a bit more than last year. So, I thought I would update last years post with my new knowledge, as well as generalize the intuition to schemes - which we introduced in the last post....

The first two posts ([1],[2]) I ever did on this blog - now over a year ago - were posts about algebraic geometry. In particular we explored the geometric implications of some of the algebraic results I was learning in my commutative algebra class. Last summer I also wrote a post about sheaves, and left it off by claiming to soon write about schemes. If you scroll through the blog we have covered a bunch of different topics, but the blog post on schemes, seems to have fallen through the cracks....