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 (S-U-3.01), Wed, 12-14 (N-U-3.05). There will be a weekly exercise session (the date will be determined later).

Moodle page for the course: link (ag3-winter-2324)

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