These are interesting times to look over the algebraic geometry arxiv postings. Just over a week ago, there was a posting by Tanaka which claimed the minimal model program was false in characteristic two. Then yesterday at the top of the page was a paper by Castravet and Tevelev claiming that the Mori Dream Space conjecture for was false. Then today, there is a paper by Fontanari claiming instead that the Mori Dream Space conjecture is TRUE for the same space, but modded out by the finite group .

December 3, 2013

## The sound you hear is another conjecture in birational geometry dropping like a fly

Posted by Jim Stankewicz under Algebraic Geometry, UncategorizedLeave a Comment

February 26, 2013

First, the oops. I DID intend to blog from Berlin. Didn’t happen, got caught up in giving talks and starting collaborations. It happens. I MAY be posting again in the next couple of months, but I’m only back home for a couple of weeks before I go off again travelling. Mid-May is the next long-term stable period I’ll have, but I have half written posts that should be up before then. Probably. Maybe.

As for “Yay” (cue youtube), the biggest reason for the “Oops” is that my thesis is finally posted to the arXiv! The next project won’t take so long.

December 9, 2012

## The Gauss Map

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry, Complex Analysis, Differential Geometry1 Comment

Posting is slowing down a bit, I’ve got a paper I’m trying to get out, and a couple of projects that are hitting some preliminary results, plus, I’m getting ready for holiday travel, and then two months at Humboldt. Trying out an experiment with more rigid personal scheduling, and hopefully I’ll post more often. Also, I’m reviewing Atiyah-Macdonald, Eisenbud, and Schenck so that perhaps in March I can begin a “Commutative Algebra from the Beginning” series, or perhaps just a series on geometric interpretation of commutative algebra theorems.

However, for today, we’re going to take something most of us first saw in differential geometry (I first met this map in do Carmo‘s book) and translate it into algebraic geometry.

November 19, 2012

## Understanding Integration III: Jacobians

Posted by Charles Siegel under Abelian Varieties, AG From the Beginning, Algebraic Geometry, Complex Analysis, CurvesLeave a Comment

Now, we’re going to talk a bit about the geometry of the periods, which were completely analytic in nature. As we mentioned, for a compact Riemann surface , we have a period matrix that encodes the complex integration theory on the surface.

October 22, 2012

## Japanese for mathematics: Algebraic Variety

Posted by Charles Siegel under Japanese for Mathematics[4] Comments

Last time on this series, I talked about the word manifold. Today, we’re going to add a modifier.

October 15, 2012

No substantive post today, because my grant application is due. New post next week!

October 15, 2012

## Understanding Integration II: 1-Forms and Periods

Posted by Charles Siegel under AG From the Beginning, Algebraic Geometry, Complex Analysis, CurvesLeave a Comment

Last time, we discussed integration theory of functions along paths on Riemann surfaces, and then we decided that we wanted to talk about compact Riemann surfaces. Unfortunately, there aren’t any holomorphic functions on them, and meromorphic functions are the wrong choice about what to integrate along curves. Today, we’ll talk about the correct things to integrate, and some of their properties.