Monthly Archives: August 2008

Integrable Systems

Posted on August 28, 2008 by Charles Siegel

As part of my project to not let orals actually degrade my sanity beyond recovery, today we’re going to do some physics! Well, kind of. We’ll be citing a lot of physics, at the least, and using it to motivate … Continue reading →

Posted in Abelian Varieties, Algebraic Geometry, Curves, Differential Geometry, Mathematical Physics | 2 Comments

Legalities Question

Posted on August 26, 2008 by Charles Siegel

Ok, this might be a silly question, but I’m not sure if something I want to do is legal or illegal. So, I’ve got some books in pdf format that are obtained legally (ie, EGA as downloaded from Numdam) which … Continue reading →

Posted in Uncategorized | 3 Comments

Group Schemes and Moduli (II)

Posted on August 24, 2008 by Matt DeLand

We continue our quest to understand when quotients of schemes by actions of group schemes exist. Last time we defined group schemes, group actions, geometric quotients, and gave some examples. In this post, I’ll define what it means to be … Continue reading →

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

Constructing Nodal Curves

Posted on August 20, 2008 by Charles Siegel

So, I don’t really have a full length post in me at the moment. However, here’s a nice trick that I’ve learned recently, plus some motivation. With this, it’s easy to write down explicitly a curve of arbitrary degree in … Continue reading →

Posted in Algebraic Geometry, Curves, Examples | 11 Comments

New Theme

Posted on August 19, 2008 by Charles Siegel

So, we’ve got a new theme. This is for one simple reason: the old one didn’t list the author of posts. This wasn’t an issue before, but today, just before this, is the first post from one of the new … Continue reading →

Posted in Uncategorized | 1 Comment

Group Schemes and Moduli (I)

Posted on August 19, 2008 by Matt DeLand

Hi! My name is Matt DeLand, I’m a graduate student at Columbia and I’m responding to Charles’ call for cobloggers. I also study Algebraic Geometry, and have been enjoying Charles’ posts; hopefully I can help out and make some positive … Continue reading →

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

Request: Projective Elimination Theory

Posted on August 14, 2008 by Charles Siegel

We talked before about elimination theory, doing it entirely in the affine case. The question was asked about how to do it projectively. There are a couple of subtleties to it, but the idea is simple: we eliminate in each … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Big Theorems, Computational Methods | 2 Comments

Less posting for a bit

Posted on August 11, 2008 by Charles Siegel

Ok, well, I’m going to be posting less, and hopefully settling into a regular schedule at some point, but the rest of the month is going to be erratic at best, with my orals being (in theory) the first week … Continue reading →

Posted in Uncategorized | 1 Comment

Phylogenetics and Algebraic Geometry

Posted on August 7, 2008 by Charles Siegel

Ok, this post is going a little bit out of my field. If anyone can fill in some of the gaps in my understanding of phylogenetics and in how to get from there to the math, please do so in … Continue reading →

Posted in Algebraic Geometry, Biology, Combinatorics, Probability | 7 Comments

Geometric Form of Riemann-Roch

Posted on August 7, 2008 by Charles Siegel

Now, the way that the Riemann-Roch theorem was phrased before, the geometry wasn’t obvious. We had to extract it in terms of rational functions with poles given by a divisor. Now that we’ve talked about canonical curves, we can use … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Big Theorems, Curves | Leave a comment