Monthly Archives: February 2010

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

Beauville makes a list

Posted on February 24, 2010 by Charles Siegel

If you like Hyperkähler manifolds (and who doesn’t?) go check out Beauville’s new preprint: Holomorphic symplectic geometry: a problem list.  It’s nice and short survey of the basic facts of hyperkähler manifolds, including a bunch of conjectures and open problems … Continue reading →

Posted in Algebraic Geometry, Open Problems | 1 Comment

The Hodge Theorem

Posted on February 22, 2010 by Charles Siegel

Previously, we talked a bit about the category of Hodge structures, and did some basic constructions.  However, I’d claimed that this was algebraic geometry (at least, in the categories on the post) so today, we’ll talk about a LOT of … Continue reading →

Posted in Algebraic Geometry, Cohomology, Hodge Theory | 2 Comments

Algebraic Geometry Belongs to Sheaves

Posted on February 5, 2010 by Charles Siegel

Over at the n-Category Cafe, Tom Leinster has written an excellent post pointing out that sheaf theory is NOT a subfield of algebraic geometry.  I feel I have a few things to add, not enough for a long post, but … Continue reading →

Posted in Algebraic Geometry, Sheaves, Uninformed Opinion | 16 Comments

Hodge Structures

Posted on February 4, 2010 by Charles Siegel

Back to blogging for a bit, though likely infrequently.  Doing a new series that might count as AG from the beginning, so I’ll put it up there once I’ve got a couple done.  We’re going to start doing some Hodge … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Cohomology, Hodge Theory | 2 Comments