Mathematical Institute of the University of Bonn

Algebraic Geometry I - Wintersemester 2013/14

Dr. Eugen Hellmann
E-mail: hellmann (add @math.uni-bonn.de)

Monday 12-14h, Thursday 10-12h, Kleiner Hörsaal, Wegelerstraße 10
First lecture: 14.10.2013

Contents

The lecture course provides an introduction to modern algebraic geometry i.e. the theory of schemes. The provisional schedule includes:

• Affine and projective algebraic sets
• Sheaf theory
• Definition of Varieties and Schemes and their basic properties
• Subschemes, products, dimension
• Coherent and quasi-coherent modules
• Vector bundles, lines bundles
• Representable functors

Prerequisites

The lecture builds on the lecture course Algebra I .
Knowledge of commutative algebra on the level of the book of Atiyah, MacDonald (including quotients, localizations, tensor products, Krull dimension, Hilbert's Nullstellensatz, Noether normalization) and knowledge of Galois theory is required.

Exercise sessions

There are weekly exercise sessions accompanying the lecture. Qualifying conditions for the exam: scoring at least 50% of the points obtainable on the exercise sheets.

Group	Time and Place	Tutor	Participants
Group 1	Monday 16-18h, Room N 0.003	Andreas Mihatsch	Group 1
Group 2	Wednesday 12-14h, Room SR 0.007	Emanuel Reinecke	Group 2

Exercise sheets

• Exercise sheet 1 due 24.10.2013
• Exercise sheet 2 due 31.10.2013
• Exercise sheet 3 due 07.11.2013
• Exercise sheet 4 due 14.11.2013
• Exercise sheet 5 due 21.11.2013
• Exercise sheet 6 due 28.11.2013
• Exercise sheet 7 due 05.12.2013
• Exercise sheet 8 due 12.12.2013
• Exercise sheet 9 due 19.12.2013
• Exercise sheet 10 due 09.01.2014
• Exercise sheet 11 due 16.01.2014
• Exercise sheet 12 due 23.01.2014
• Exercise sheet 13 due 30.01.2014

Exam

The exam takes place in the last lecture: 06.02.2014, 10-12h, Kleiner Hörsaal, Wegelerstraße 10.
The exam and the solutions (partly a bit sketchy) can be found here.
Second exam: 31.03.2014, 10-12h, Kleiner Hörsaal. Please be at the lecutre hall at 09:50h so that we can start on time. You need to bring a pen and an ID.
You can have a look at the exam and the corrections on Tuesday April 1st, 11-12h in the Hausdorffraum.

References

• U. Görtz, T. Wedhorn: Algebraic Geometry I , Springer Vieweg
• A. Grothendieck, J. Dieudonné: Éléments de Géométrie Algébrique I-IV, Publ. Math. IHES
• R. Hartshorne : Algebraic Geometry, Springer
• D. Mumford: The Red Book of Varieties and Schemes, Springer

---

Last modified: 06. 02. 2014, Eugen Hellmann