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Arbeitsgruppe Algebra

Algebraic Geometry (Fall term 2021)


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).


Among the many books and manuscripts about algebraic geometry, I will mainly use the follows one. Here is a (very incomplete) list of further references.

  • 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

Exercise classes

There will be a weakly excercise sheet related to the content of the lecture. It is highly recommended to solve the exercises in order to understand the material from the lecture properly. These exercises will be discussed in a weekly exercise class, in which you can also ask any other question related to the content of the lecture. Exercise classes will be be done via Zoom as well, every Tuesday, 13.45-15.15.