Monthly Archives: March 2009

Schubert Classes and Cellular Cohomology

So, as of the last post in the series, we defined Schubert cells.  We’re going to use them to discuss the Cohomology of the Grassmannian, and to write down an explicit basis.  With an eye looking forward, next time, we’ll … Continue reading

Posted in Algebraic Geometry, Algebraic Topology, Cohomology, Combinatorics, Computational Methods, Enumerative Geometry, Intersection Theory, Uncategorized | 6 Comments

The Weil Pairing

A nice thing about elliptic curves is the wealth of information which is tied up in the isomorphism class of the group. Over the complex numbers, every elliptic curve is where is a lattice of rank 2 contained in the … Continue reading

Posted in Abelian Varieties, AG From the Beginning, Curves, Uncategorized | 3 Comments

The Chow Ring and Chern Classes

Hopefully this will be the last background information post before we state and begin the proof of the Riemann Roch Theorem.  This post will be a brief overview of Cycles, Chow Rings, and Chern Classes and their properties.  The briefness … Continue reading

Posted in Uncategorized | 2 Comments

Schubert Varieties

It’s been awhile since the last post, but Spring Break happened.  Anyway, back to Schubert Calculus! Last time, we discussed Grassmannians, this time, we’re going to talk about their most important subvarieties, the Schubert Varieties.

Posted in Algebraic Geometry, Algebraic Topology, Cohomology, Combinatorics, Computational Methods, Enumerative Geometry, Intersection Theory | 5 Comments

The Dual Isogeny II

Apologies that I haven’t been posting recently. Sage days was this past weekend along with 6 inches of snow in Georgia(read: power outages), the Arizona Winter school in a week and everything else, it’s been very busy.

Posted in Abelian Varieties, AG From the Beginning, Curves, Uncategorized | 1 Comment