Category Archives: Vector Bundles

Monodromy Representations

Posted on February 25, 2010 by Charles Siegel

A departure from directly working with varieties, we’re going to do something that’s strictly topological (at first glance) but which really has deep and important connections with Hodge theory. We’re going to talk about monodromy and monodromy representations. Let be … Continue reading →

Posted in Algebraic Geometry, Algebraic Topology, Cohomology, Hodge Theory, Vector Bundles | 9 Comments

B-N-R Part 5: Spectral Curves

Posted on September 10, 2009 by Charles Siegel

Today we’re back to some material from the first post in this series, and going to prove an actual theorem about vector bundles.  Next time, we’ll be getting into the heart of the paper, and that may be my last … Continue reading →

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles | 4 Comments

B-N-R Part 4: Prym Varieties

Posted on September 9, 2009 by Charles Siegel

The last post was on the generalities of Abelian varieties, and constructing a map.  This time, we’re going to do it for a specific one, and the maps involved will all be useful later.  We start out with a finite … Continue reading →

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles | Leave a comment

B-N-R Part 3: PPAV’s and some details

Posted on September 9, 2009 by Charles Siegel

Now, we continue our tour through Beauville, Narasimhan, Ramanan.  We’ve talked about Twisted Endomorphisms and we’ve talked about the Generalized Theta Divisor on the Moduli Space of Vector Bundles.  So today we’ll talk a bit about Abelian Varieties, Principal Polarizations, … Continue reading →

Posted in Abelian Varieties, Algebraic Geometry, Big Theorems, Curves, Vector Bundles | 2 Comments

B-N-R Part 2: Moduli of Vector Bundles

Posted on August 25, 2009 by Charles Siegel

Last time, we talked about twisted endomorphisms.  Now, we’re moving on to the second paragraph of the paper: generalized theta divisors.  In the meantime, we’re going to have to talk a bit about vector bundles and their moduli.

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles | 2 Comments

B-N-R Part 1: Twisted Endomorphisms

Posted on August 24, 2009 by Charles Siegel

Alright, I’m back, and newly married (thus the long hiatus from posting).  And now it’s time to get back to math.  I’m currently attempting to read a paper by Beauville, Narasimhan and Ramanan titled “Spectral Curves and the Generalized Theta … Continue reading →

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles | 5 Comments