ANAGRAMS

Student seminar

Goal

The goal would be to familiarise with the classical theory of Chern classes in algebraic geometry using both Fulton's and Grothendieck's approach, discuss interesting examples, and maybe discuss noncommutative generalisations of the theory.

For some references, consider the absolute classic [1] by Fulton, the more accessible notes by Gathmann [2] (chapters 9 and 10) or Teitler [5], the unfinished (but excellent) text book [4] and Grothendieck's article [3].

Schedule

October 9
Introduction to characteristic classes (blogpost)
A primer on the Chow ring of a variety
by Pieter Belmans and Julia Ramos Gonzalez, in G.015, at 13h00
October 16
Chern classes à la Grothendieck (notes)
by Theo Raedschelders, in G.015, at 13h00
October 23
Computing with Chern classes
Twenty-seven lines on a cubic surface
By Frederik Caenepeel and Julia Ramos Gonzalez, in G.015, at 13h00
October 30
The additive struture of the Chow ring of a Grassmannian (notes)
The multiplicative struture of the Chow ring of a Grassmannian (diagrams)
By Jens Hemelaer and Pieter Belmans, in G.015, at 13h00

References

[1]
Fulton, William
Intersection theory
Springer, 1983, xiii+470
[2]
Gathmann, Andreas
Algebraic geometry (online)
[3]
Grothendieck, Alexander
La théorie des classes de Chern
Bulletin de Société mathématique de France, 1958, 137–154
[4]
Eisenbud, David and Harris, Joe
3264 & all that: intersection theory in algebraic geometry
unfinished text book, available online
[5]
Teitler, Zach
An informal introduction to computing with Chern classes in algebraic geometry (online)