Algebraic Geometry II (WiSe 2024-25)
Lecturer:
Prof. Dr. Bruno Klingler
Time and place:
Wed 9am-11am 1.115
Thu 11am-13am 1.115
Wed 1pm-3pm 3.006 (Exercises, Ania Otwinowska)
The class will start on October 16th.
Moodle:
The Moodle page for the course is here , you can register there.
The Moodle key is AlgGeo.
Content:
The plan of the course is the following:
- complements on quasi coherent sheaves and cohomology
- studying subschemes (multiplicity, formal completion, construction)
- Kaehler manifolds
- Hodge theory and vanishing theorems
- GAGA
- Algebraic de Rham cohomology
- Serre duality
- Chern classes
- Deformation theory
- flatness
- higher direct images
-
I will not follow a particular book.
The following references are relevant:
- P. Griffiths, J. Harris: Principles of algebraic geometry. Wiley
- J.De Jong and collaborators: The Stacks project
- D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197,
Springer.
- U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg.
- A. Grothendieck, J. Dieudonné: Éléments de géométrie algébrique.
- R. Hartshorne: Algebraic Geometry GTM 52. Springer.
- D. Mumford: The Red book of varieties and schemes. Springer LN 1358.
- R. Vakil: Foundations of algebraic geometry. Online lectures
- C. Voisin: Hodge theory and complex algebraic geometry I,
II. Cambridge Univ.Press