Category Archives: Complex Analysis

The Gauss Map

Posted on December 9, 2012 by Charles Siegel

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 … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Complex Analysis, Differential Geometry | 2 Comments

Understanding Integration III: Jacobians

Posted on November 19, 2012 by Charles Siegel

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 … Continue reading →

Posted in Abelian Varieties, AG From the Beginning, Algebraic Geometry, Complex Analysis, Curves | 2 Comments

Understanding Integration II: 1-Forms and Periods

Posted on October 15, 2012 by Charles Siegel

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 … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Complex Analysis, Curves | Leave a comment

Understanding Integration I: Riemann Surfaces

Posted on October 1, 2012 by Charles Siegel

I’m back! And now, posting from Kavli IPMU in Japan.  Now, I’m going to start a series on theta functions, Jacobians, Pryms, and abelian varieties more generally, hopefully with some applications, with my goal being at least one post a … Continue reading →

Posted in Abelian Varieties, AG From the Beginning, Algebraic Geometry, Complex Analysis, Curves | 5 Comments