Rambling Thoughts on Geometry

October 15, 2009 by

I am not sure that everyone in the class has been exposed to “classical” algebraic varieties.  Without some background here,  I would think it would be hard to understand why we are doing anything we are doing in class.  So I hope that we can use this space to write up rambling thoughts on the underlying geometry here.

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Exercises from Hartshorne

October 13, 2009 by

Work out Hartshorne exercises here!

Chapter 1 – Fulton

October 13, 2009 by

Discussion of exercises from Algebraic Curves – Chapter 1 – Fulton

Here is a link to the book:

http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf

Long LaTeX posts in WordPress.com

October 9, 2009 by

WordPress does a good job supporting simple LaTeX expressions. You type $ latex 2^{2^k}$, and out comes 2^{2^k}.  Although adding “latex” in the middle of the dollar signs  is a slice difference between latex commands, when your have dozens of formulas in you article or your want to edit a long latex script to wordpress format, it definitely cost some labor, which is unnecessary as I believe.  No mention that we often need more complicate commands, such as numbering the equation. Since these differences between latex and wordpress have some patterns, they can be eliminated by programming as one can expect. I glad some one did put some effort  on the project:

There is a simple tool to convert your latex script  to html that can be pasted directly.

LaTeX2WP, written by Luca Trevisan, is a Python script that will convert a LaTeX file into a format suitable for pasting into a WordPress.com post. Hence you need Python, which is automatically embedded in Unix, Mac OS and Linux(all distributions), in your system.  Just click the link to see the details and instructions.  Please Make sure to download the latest version.

I have tried it several times and am aware that how to revise the python script to fit part of your latex preamble. In fact, due to the restrictions from wordpress and the current work load of the author, there are many latex commands and packages which is not supported, so the best way is to follow his definition in the style files.

If your like it, or have any questions, welcome to discuss with me.

Yang Liu (liu@math.osu.edu)

On Hilbert’s Nullstellensatz (a non HW post)

October 8, 2009 by

Just to kick things off…

I just thought that I’d like to point out a blog entry of Terry Tao’s on the Hilbert Nullstellensatz. It makes for interesting reading and also takes (what I think is) a more concrete approach, eschewing the formidable algebraic machinery that took us nearly 2 weeks to cover.

Click on the Link

Also, Wikipedia has a nice entry on the theorem, with an auxilary entry on the Rabinowitsch trick.

If you click here, you’ll find an expository paper of Richard Swan based on an ‘elementary’ proof of the Nullstellensatz by Ritabrata Munshi. I particularly like the way how different approaches all give us different interpretations of the Nullstellensatz itself.

Discuss Homework 1 here!

October 5, 2009 by

– Problem list goes here –

Hello world!

October 2, 2009 by

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