# Lecture Course Algebraic geometry 3 (Winter 2023/24)

## Algebraic geometry 3

This is the continuation of my Algebraic geometry 2 class (but of course everybody is welcome to join, regardless of whether you attended that class).

A list of topics I would like to discuss is

- Sheaves of differentials, smooth and étale morphisms
- Serre duality
- Cohomology and base change
- Grassmannians and flag varieties
- Hilbert schemes

The list could be adapted depending on background knowledge and/or preferences of the participants.

**Prerequisites:** Basics of scheme theory, foundations of the theory of cohomology of abelian sheaves and (quasi-coherent) $\mathscr O_X$-modules as covered in Algebraic geometry 1, Algebraic geometry 2 In terms of Hartshorne’s book, Sections II.1 – II.7 and III.1 – III.5 are more than enough. In terms of my books with Wedhorn, Chapters 2 – 5, 7 – 11, 21 – 23 cover (almost) everything we did in class (and a lot that we did not discuss).

**Dates:** Mon, 10-12, Wed, 12-14. There will be a weekly exercise session (the date will be determined later).

**Moodle page for the course:** … forthcoming …

**Contact:** Ulrich Görtz, `ulrich.goertz@uni-due.de`