So now we begin one of the great examples in algebraic geometry: algebraic groups. These are exceptionally nice, and we’ll talk about a couple of more general concepts before applying them to this case.

### December 2007

December 22, 2007

## Algebraic Groups

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry, Examples[8] Comments

December 21, 2007

## Morphisms of Varieties

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry[3] Comments

Last time we brought in a bunch of the algebra necessary to do algebraic geometry, now we’ll talk a bit about topology, a bit about morphisms, and then note that we have a perfectly well-defined category (and we’ll even say what that means).

December 20, 2007

## Some Commutative Algebra and a bit of Geometry

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry[6] Comments

Before moving on to morphisms of varieties, it would do us some good to talk about a bit of commutative algebra and to do a little bit more geometry of individual objects. The central notion of algebra that we’ll be needing is that of a *commutative ring with identity*.

December 18, 2007

## Projective Varieties

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry[4] Comments

Yesterday, there was talk of affine varieties, and I pointed out the fact that intersections don’t work out nicely in this case. Today we’ll talk about an elegant solution to this problem: the notion of projective space.

December 18, 2007

## Affine Varieties

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry[13] Comments

Ok, I know I haven’t posted in a bit, but it’s the end of my first semester of my first year, so hopefully I can be forgiven. Today, we’re going to start a (potentially doomed from the start) project: algebraic geometry without prerequisites, or at least, with minimal prerequisites. The goal is to get as much done as possible, with detours into many of the more interesting theorems, and today we’re going to start with affine varieties.