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)

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