Algebraic Geometry (GALG 132646)
Timetible
Tuesday and Thursday 14h - 16h, online.
Exercises
Exercises in this
sheet are due for May 20th.
Date of the oral presentations
The student shall present their dissertations on July 1st. We will meet online according the following schedule:
| Name |
Time |
Title |
| Pedro Silva |
9h - 9h45 |
The Riemann-Roch Theorem |
| João Candeias |
10h - 10h45 |
Blow-up and the normal cone degeneration |
| Robert Hanson |
11h - 11h45 |
Abelian Fourier-Mukai transforms and sheaves on elliptic curves |
| Pedro Magalhães |
13h - 13h45 |
The Hard Lefschetz Theorem |
| Javier Orts |
14h - 14h45 |
Hodge structures |
Topics for the dissertation
The student should choose one topic among those contained in this
sheet and write a short dissertation to be delivered by June 22nd.
List of topics
Along the course we shall follow Prof. Andreas Gathmann's notes, that can be found in his
website.
- Introduction: notes, slides.
- Affine varieties: notes, slides, video.
- The Zariski topology: notes, slides.
- The sheaf of regular functions: notes, slides, video.
- Morphisms: notes, slides.
- Varieties: notes, slides, video.
- Projective varieties I: notes, slides, video.
- Projective varieties II: notes, slides, video.
- Grassmannians: notes, slides, video.
- Birrational transformations and blow-up: notes, slides, video.
- Smooth varieties: notes, slides, video.
- Schemes: notes, slides, video.
- Sheaves of modules: notes, slides, video.
- Quasi-coherent sheaves: notes, slides, video.
- Differentials: notes, slides, video.
- Sheaf cohomology: notes, slides, video.
- Proj construction: notes from Chapter 4.5 of [V], slides, video.
- Derived functors: notes from Part III, Chapter 1 of [Ha], slides, video.
- Serre duality: notes Part III, Chapter 7 of [Ha], slides, video.
- Flatness: notes from Part III, Chapters 8 and 9 of [Ha], slides, video.