Algebraic Geometry (Fall term 2021)
Content
The aim of this lecture is to introduce basic concepts of modern algebraic geometry. These include- Affine algebraic varieties
- Dimension and components of algebraic varieties
- Spectra of rings
- Sheaves and schemes
- Local rings, Zariski tangent spaces, singularities
- Projective varieties
- Quasi-coherent sheaves of modules
This lecture will be given in either German or English, depending on the audience.
There will be a weekly exercise sheet. Working actively on solving the problems from these sheets is an essential part of the lecture.
Prerequisits for this lecture is a good account of the content of the lectures " Lineare Algebra 1 und 2" and of an undergraduate class in " Algebra" (especially basics about ring theory and the theory of field extensions are useful).
Literature
Among the many books and manuscripts about algebraic geometry, I will mainly use the follows one.- Ulrich Görtz, Torsten Wedhorn: Algebraic Geometry I: Schemes, Springer Verlag
- David Eisenbud: Commutative Algebra with a View Towards Algebraic Geometry, Springer-Verlag
- Wolfgang Soergel: Kommutative Algebra und Geometrie, Lecture notes
- Igor R. Shafarevich: Basic Algebraic Geometry, Band 1 und 2, Springer-Verlag
- Robin Hartshorne: Algebraic Geometry, Springer-Verlag
- David Eisenbud, Joe Harris: The Geometry of Schemes, Springer-Verlag
- Gert-Martin Greuel, Gerhard Pfister: A Singular introduction to commutative algebra
- David Eisenbud u.a.: Computations in algebraic geometry with Macaulay 2
- Andreas Gathmann Algebraic Geometry
- Olivier Debarre Introduction à la géométrie algébrique
Lecture and exercises
This lecture will be done via video conference, using the Zoom plattform. Please enroll at the OPAL course, where you will also find any other information related to the lecture (excercise sheets, access codes for video conferences etc.). Time slots for the lectures are:- Monday, 11:15–12:45
- Wednesday, 13:45–15:15