Algebraic Geometry II, Summer semester 2019
Lecturer: Georg Oberdieck
Assistant: Emma Brakkee
Tutors: Thorsten Beckmann, Matthew Dawes
Note 1: The room of Thorsten Beckmann's tutorial, Tuesdays 10-12, has been changed from 0.008 to N0.003.
Note 2: The second midterm exam has been cancelled. Instead, we will have a review problem sheet that counts for 100 points.
Monday 16:00 c.t. - 18:00, Kleiner Hörsaal (Wegelerstrasse 10)
Thursday 16:00 c.t. - 18:00, Kleiner Hörsaal
First day of class: April 1.
Fridays 11-12 am in 1.028.
The course introduces the modern language of algebraic geometry: sheaves, schemes, cohomology.
Commutative Algebra, Algebraic Geometry I (see syllabus of the first semester).
- R. Hartshorne, Algebraic Geometry.
- R. Vakil, Foundations of algebraic geometry. Online lectures.
- Qing Liu, Algebraic Geometry and Arithmetic Curves.
- U. Goertz, T. Wedhorn: Algebraic Geometry I.
|Tuesday||10:00 c.t. - 12:00||N0.003||Thorsten Beckmann|
|Tuesday||12:00 c.t. - 14:00||0.003||Matthew Dawes|
|Wednesday||14:00 c.t. - 16:00||1.008||Matthew Dawes|
Problem sets & midterm exams
There will be one problem set every week.
Solutions to the exercises are to be handed in every Monday before the lecture.
The solutions are submitted individually, group submissions are not allowed.
The problem sets are 50 points each.
There will be two midterm exams that replace the exercise sheets the given week. They are 45 minutes in class exams, 100 points each.
One has to have half of the total numbers of points to be admitted to the final exam.
The exam is a 2 hour written exam. The dates are as follows.
- Final exam 1: Wednesday, July 24, 9:00 - 11:00, Großer Hörsaal.
- Final exam 2: Monday, September 23, 9:00 - 11:00, Kleiner Hörsaal.
List of problem sets and midterm exams
Problem set 1, due April 8.
Correction: in the second line of Problem 3, the third term in the short exact sequence should be I/F, not F/I.
Solutions for problem set 1. Correction: new (correct) proof of Problem 1(a).
Problem set 3, due April 29.
Corrections: in Problem 3(b), one has to assume that X is noetherian, otherwise the statement is false.
this MathOverflow post.
In Problem 4(c), You may use that H^1(X,O_X*) can be computed using Čech
In the hint for Problem 5, the tensor product of the
complexes is homotopy equivalent to the Čech complex for the tensor product.
Solutions for problem set 3.
Problem set 10, due July 8.
Correction: In Problem 2(c), calculate the cohomology of the structure sheaves of the fibres.
In Problem 1(c), the equation of the curve should be y^2=x^3+x^2.
Solutions for problem set 10. Correction: Corrected Problem 2.