April 2009

Monthly Archive

April 22, 2009

Quaternion Algebras and Modular Forms

Posted by Jim Stankewicz under Talks
[4] Comments 

Dear readers,

I know I promised a post  on modular curves, but I had to devote more time to my end of semester project. Since it’s strongly related to the topic of modular curves and I present on it tomorrow, I decided to make this post in the seminar talks category.

(more…)

 

April 20, 2009

Pieri and Giambelli Formulas

Posted by Charles Siegel under Algebraic Geometry, Algebraic Topology, Cohomology, Combinatorics, Computational Methods, Enumerative Geometry, Intersection Theory, Uncategorized
1 Comment 

It’s been a few weeks, but now I’m back and today we’ll talk about the multiplication in the cohomology ring of Grassmannians.  Though we won’t talk about the Littlewood-Richardson rule in its full glory, we will howver discuss the special cases of the Pieri rule and the Giambelli formula.

(more…)

 

April 5, 2009

The Grothendieck-Riemann-Roch Theorem, Stated

Posted by Matt DeLand under Algebraic Geometry, Big Theorems, Cohomology, Intersection Theory
[5] Comments 

Suppose you have a proper map f:X \rightarrow Y between smooth (quasi) projective varieties.  Then suppose you have a coherent sheaf F on X.  After viewing that sheaf as an element of the Grothendieck Group of coherent sheaves on X, there are two things you could do.  The first thing is that you could push forward this element to the Grothendieck Group on Y, and then take its chern character, to arrive at an element in the Chow Ring of Y.  The second option you have is to first take the chern character of F in the Chow Ring of X, and then push it forward to the Chow Ring of Y.  Now we have two elements in the Chow Ring of Y and we could wonder if we have the same element.  The Grothendieck Riemann Roch (GRR) Theorem tells us we don’t quite have the same element, but it tells us exactly by how much we are off!

(more…)

 

Follow

Get every new post delivered to your Inbox.

Join 88 other followers