Monthly Archives: December 2007

Algebraic Groups

Posted on December 22, 2007 by Charles Siegel

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.

Posted in AG From the Beginning, Algebraic Geometry, Examples | 10 Comments

Morphisms of Varieties

Posted on December 21, 2007 by Charles Siegel

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 … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry | 4 Comments

Some Commutative Algebra and a bit of Geometry

Posted on December 20, 2007 by Charles Siegel

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 … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry | 6 Comments

Projective Varieties

Posted on December 18, 2007 by Charles Siegel

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.

Posted in AG From the Beginning, Algebraic Geometry | 5 Comments

Affine Varieties

Posted on December 18, 2007 by Charles Siegel

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 … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry | 15 Comments