Mathematical Institute of the University of Bonn

Algebraic Geometry I

Lecturer: Georg Oberdieck

Assistant: Matthew Dawes

Tutors: Thorsten Beckmann, Isabell Grosse-Brauckmann, Lisa Li , Hsueh-Yung Lin, René Mboro

Classes

Montag: 16:00 c.t. - 18:00 Uhr, Kleiner Hörsaal Wegelerstrasse 10;

Donnerstag: 16:00 c.t. - 18:00 Uhr, Kleiner Hörsaal Wegelerstrasse 10

First day of class: October 11.

Content

The course introduces the modern language of algebraic geometry: sheaves, schemes, cohomology.

Pre-requisites

A basic knowledge of commutative algebra (prime ideals etc).

Syllabus

Course syllabus

References

D. Mumford: The Red book of varieties and schemes. Springer LN 1358. R.

U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg.

R. Hartshorne: Algebraic Geometry GTM 52. Springer.

D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197, Springer.

Vakil: Foundations of algebraic geometry. Online lectures.

Shafarevich, Basic Algebraic Geometry I + II.

Tutorials

Tue 10-12, Neubau N 0.007

Tue 10-12 Uhr AVZ1 SR7 (Raum 0.001)

Wed 2-4, Neubai N 0.008

Problems

There will be one problem set every week. Solutions to the exercises are to be handed in every Monday before the lecture.

Solutions are to be submitted individually. i.e. not in groups.

The solutions will be graded by points. One has to have half of the points to be admitted to the final exam.

There will be two midterm exams (45 minutes in class exams) that replace the exercise sheets the given week and count toward the total point score.

Prüfung Algebraic Geometry I

Final Exam I: 07.02.19, 9-11, Großer Hörsaal,

Final Exam 2: 18.03.19, 9-11, Großer Hörsaal.

This is a written exam

Mailing list

You can subscribe to an email mailing list in order to receive updates and information on classes, tutorials, and problem sheets. Subscription is non-compulsory, but strongly encouraged. In order to subscribe, please follow the instructions here .

Office hours

Friday 2-3pm in 1.028.

List of problem sets and midterm exams

Please report errors or misprints to mdawes@math.uni-bonn.de.

Oct 15: -

Oct 22: PS1 due

Problem Sheet 1

Solutions to Problem Sheet 1

Oct 29: PS2 due

Problem Sheet 2

Solutions to Problem Sheet 2

Nov 5: PS3 due

Problem Sheet 3

Solutions to Problem Sheet 3

Nov 12: Midterm 1

Midterm I practice problems

Solutions to Midterm I practice problems

Nov 19: PS4 due

Problem Sheet 4

Solutions to Problem Sheet 4

Nov 26: PS5 due

Problem Sheet 5

Solutions to Problem Sheet 5

Dec 3: PS6 due

Problem Sheet 6

Solutions to Problem Sheet 6

Dec 10: PS7 due

Problem Sheet 7

Solutions to Problem Sheet 7

Dec 17: Midterm 2

Midterm II practice problems

Christmas Problem Sheet

Jan 7: -

Jan 14: PS8 due

Problem Sheet 8

Solutions to Problem Sheet 8

Jan 21: PS9

Problem Sheet 9

Solutions to Problem Sheet 9

Jan 28: PS10.

Problem Sheet 10

Solutions to Problem Sheet 10

Exam practice problems

There will be 50 points per problem set and 100 points per mid-term exam. One needs a total of 350 points to be admitted to the final exam.