# Monthly Archives: November 2009

## Everything is a Normal Cone

Well, really, for intersection theory, it’s true.  We start with a closed subscheme, with normal cone .  We’re going to construct a family of embeddings that deforms to the zero section of .  Then, because intersections should vary nicely in … Continue reading

Posted in Intersection Theory, MaBloWriMo | 2 Comments

## Segre Classes of Subschemes and their Applications

So, last time we talked about Segre classes and cones.  Now, we’re going to move ahead, and talk about a specific cone in detail, the Normal cone we defined on Monday.  Let be a subscheme, and let be its normal … Continue reading

Posted in Intersection Theory, MaBloWriMo | 2 Comments

## Segre Classes of Cones

Last time, we talked about the Normal Cone.  We’re going to go back a bit and increase the generality before coming back to it.  Let be a cone over , and let be the projective closure.  We define the Segre … Continue reading

## Normal Cones

Ok, so I took the weekend off to figure out where things are going and get a bit ahead.  Will probably be doing that all month.  So now, we’re going to talk about cones and normal cones, with the goal … Continue reading

Posted in Intersection Theory, MaBloWriMo | 1 Comment

## Chern Character and K-Theory

Today, we’re going to construct a ring that encodes quite a lot of intersection data (though not terribly transparently) as well as some special combinations of Chern classes.  A lot of modern intersection theory and enumerative geometry takes place in … Continue reading

Posted in Intersection Theory, MaBloWriMo | 3 Comments

## Chern Classes: Part 2

We’ve define the Chern classes now, but what about computing them, and computing with them? We have that long list of properties that will help, but there is a need to prove them, and they aren’t completely trivial.  What we … Continue reading

Posted in Intersection Theory, MaBloWriMo | 2 Comments

## Some Technical Points

So, I’ve been a bad math blogger.  I’ve been identifying a bunch of different classes of things that we can really only identify on nice algebraic schemes.  Things like smooth varieties (where I’ve grabbed all of my examples).  There are … Continue reading