Algebraic Geometry I (V4A1), Winter semester 2015/2016

Dozent: Prof. Daniel Huybrechts

Assistent: Andrey Soldatenkov

The course will be taugth in English. It is recommended to all Bachelor students who plan to write a bachelor thesis in algebraic geometry in the workgroup.
Part II will be taugth in the following term.

This course is an introduction to the language of schemes (including sheaves and their cohomology), which are (ringed) spaces that locally look like the spectrum of a commutative ring. This is the language of modern algebraic geometry and was mainly developed by Grothendieck. The focus of the course will really be on schemes and not so much varieties (which will only be touched upon occasionally). Prerequisite for this course is a good knowledge of commutative algebra (to the extent of last term's course Algebra I).
One of the founders of the theory, David Mumford, wrote in 1975:
[Algebraic geometry] seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics! In one respect this last point is accurate ...
Find out!

Lectures

Monday 12.00 - 14.00, Großer Hörsaal, Wegelerstr. 10 and Thursday 14.00 - 16.00, Kleiner Hörsaal, Wegelerstr. 10

  • Literature:
    • R. Hartshorne: Algebraic Geometry GTM 52. Springer. (This is still the most commonly used source.)
    • D. Mumford: The Red book of varieties and schemes. Springer LN 1358.
    • R. Vakil: Foundations of algebraic geometry. Online lectures
    • J. de Jong: The Stacks project
    • D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197, Springer.
    • U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg.
    • Q. Liu: Algebraic Geometry and Arithmetic Curves. Oxford GTM

Exams:

  • 23.02.2016, 13.00 - 15.00, Großer Hörsaal, Wegelerstr. 10;
  • 31.03.2016, 9.00 - 11.00, Kleiner Hörsaal, Wegelerstr. 10.

Exercise sheets

Solutions of the exercises have to be handed in every Monday before(!) the lecture.
One has to collect half of the points to be admitted to exams.

Tutorials

Tutorials will start on Wednesday, 28.10.2015. Registration for the tutorials will take place on Monday, 19.10.2015 at the lecture.

Monday Tuesday Wednesday Thursday Friday
8-10 1
10-12 3
12-14
14-16 2
16-18
18-20 4

Group Time Room Tutor/-in
1 We 8-10 1.008 Kai Behrens
2 We 14-16 0.006 Paul Görlach
3 Fr 10-12 0.007 Isabell Große-Brauckmann
4 Th 18-20 0.008 Matthias Weirich

Tutorial groups

We apologize for misprints in the names.

  • Group 1 (We 8-10, room 1.008)
    • Kevin Li
    • Simon Omlov
    • Orlando Marigliano
    • Mohammad Talehi
    • Jonathan Gruner
    • Uran Meha
    • Giorgi Vardosanidze
    • N-Ripinyay Achanya
    • Gordon Hausmann
    • Malte Fromming
    • Stefan Rettenmayer
    • Felix King
    • Theocharis Papantonis
    • Benjamin Lehmann
    • Pascal Beyer
    • Tobias Töpfer
    • Pagona Konlakidon
    • Lukas Heidemann
  • Group 2 (We 14-16, room 0.006)
    • Anna Arutjunova
    • Michael Stahlhauer
    • Lars Maiev
    • Georg Kempa
    • Samed Düzlü
    • Arsen Shebzukhov
    • Patrick Schnibben
    • Marvin Kohlmann
    • Fabian Hoppe
    • Aran Tattar
    • Axel Kölschbach
    • Lars Munser
    • Raffaella Mulas
    • Matthias Koch
    • Daniel Rehn
    • Marins Gramb
    • Eric Hahn
    • Salvatore Flocceri
    • Thilo Baumann
    • Janos Meny
    • Mafalda Milheiro Marques da Silva Santos
    • João Lourenço
  • Group 3 (Fr 10-12, room 0.007)
    • Alexis Machad
    • Benjamin Ruppik
    • Max Rath
    • Simone Fabbrizzi
    • Stefano Ariotta
    • Annika Kiefner
    • Anno Kurth
    • Yuqing Shi
    • Pablo Magni
    • Qidi Wang
    • Bartiomiej Kielak
    • Ho Yin Leung
    • Nikolaos Tsakanikas
    • Nils Waßmuth
    • Max Weissenbacher
    • Fabian Koch
    • Alexandru Ciolan
    • Domenico Volloni
    • Giulio Lo Monaco
    • Shanxiao Huang
    • Thi Quynh Trang Nguyen
  • Group 4 (Th 18-20, room 0.008)
    • Fabian Leuzeu
    • Robin Stoll
    • Tobias Lenz
    • Vincent Gajda
    • Thorsten Beckmann
    • Christian Singendonk
    • Christoph Spenke
    • Tim Bülles
    • Sofia Lois
    • Jason Hu
    • Paul Hege
    • Jonas Jansen
    • Ester Cabezuelo Fernández
    • Tim Seynnaeve
    • Jerian Meuleureta
    • Josua Sassen
    • Berto Natura
    • Jürgen Kanzler
    • Malte Leip
    • Benedikt Fluhv
    • Biagio Paparella
    • Alexis Marchand