### About this blog

Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.

Header is taken from the larger work by fdecomite under the creative commons license.

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# Monthly Archives: December 2007

## Algebraic Groups

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

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

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

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

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