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 things. After all, a lot of cool stuff is coming into algebraic geometry via physics these days, and the best way to understand how these things fit is to understand at least the basics of the physics.

### August 2008

August 28, 2008

## Integrable Systems

Posted by Charles Siegel under Abelian Varieties, Algebraic Geometry, Curves, Differential Geometry, Mathematical Physics[2] Comments

August 26, 2008

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 are rather out of print. I’d like to have nice copies of them to keep on my shelf and use as references…I don’t have an ebook reader, so I still prefer dead tree format. Now, there are companies like Lulu which will essentially take a PDF and convert it into an actual book, and are able to do print runs of 1, or 5, or however small. (At least, that’s my understanding)

So my question is: is it legal to have a company like Lulu print a copy of EGA (or similar out of print book) for personal use, with it not being set up to sell it to anyone else or to make a profit for me in any way?

If anyone out there actually knows what the laws on matters like this are, please help out and let me know if I’m allowed to do this.

August 24, 2008

## Group Schemes and Moduli (II)

Posted by Matt DeLand under AG From the Beginning, Algebraic Geometry, Examples[6] Comments

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 a reductive group scheme. To give a full treatment of the theory of reductive group schemes here is impossible, so we’ll pick one way to define the notion of a reductive group scheme, state some equivalences, and give some examples. I apologize for the long time between the posts, I’m on vacation and have been have been spending more time outside than at a computer!

August 20, 2008

## Constructing Nodal Curves

Posted by Charles Siegel under Algebraic Geometry, Curves, Examples[11] Comments

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 the plane, which has specified nodes. (So long as it’s possible to have that many nodes.)

August 19, 2008

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 cobloggers, Matt DeLand, from Columbia. The two themes seem close enough…comment here if there’s any trouble reading it or the like.

August 19, 2008

## Group Schemes and Moduli (I)

Posted by Matt DeLand under AG From the Beginning, Algebraic Geometry, Examples[5] Comments

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 contributions. I apologize in advance for the quality of my first post….

August 14, 2008

## Request: Projective Elimination Theory

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry, Big Theorems, Computational Methods[2] Comments

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 affine chart and then glue together. The problems that arise most naturally here actually involve working on , and projecting down to the affine space.