Algebraic Geometry II (V4A2), Summer semester 2016

Dozent: Prof. Daniel Huybrechts

Assistent: Andrey Soldatenkov

This is a continuation of Algebraic Geometry I last term. We study further properties of schemes and morphisms. Central notions like flatness and smoothness will be investigated. We will also see all the techniques applied to geometrically concrete situations.

Prerequisits: Sheaves, cohomology of sheaves, schemes, Proj and Spec, coherent sheaves, properties of morphisms (proper, separated, projective).

Lectures

Monday 16.00 - 18.00, Großer Hörsaal, Wegelerstr. 10 and Thursday 14.00 - 16.00, Großer 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:

• 02.08.2016, 9.00 - 11.00, Großer Hörsaal, Wegelerstr. 10;
• 28.09.2016, 9.00 - 11.00, Großer 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.

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4 Correction: in exercise 20 we have to exclude the case n=2, d_1=1, d_2=2. You may assume for simplicity that d_1, d_2 > 1.
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8 In exercise 38 assume additionally that k is algebraically closed and X is proper
• Sheet 9
• Sheet 10
• Sheet 11
• Sheet 12
• Preparing the exam: basic questions

Tutorials

Tutorial groups

We apologize for misprints in the names.

• Group 1 (We 14-16, room 0.008)
  
• Malte Leip
• Pablo Magni
• Paul Hege
• Fabian Lenzen
• Pagona Koulakidou
• Aran Tattar
• Nikolaos Tsakanikas
• Benjamin Lehmann
• Stefano Ariotta
• João Lourenço
• Simone Fabbrizzi
• Orlando Marigliano
• Max Rath
• Vincent Gajda
• Shanxiao Huang
• Josua Sassen
• Janos Meny
• Axel Kölschbach
• Group 2 (Th 12-14, room 1.007)
  
• Tobias Töpfer
• Fabian Koch
• Uran Meha
• Tobias Lenz
• Samed Düzlü
• Anna Arutjunova
• Michael Stahlhauer
• Mafalda Santos
• Jonathan Gruner
• Tim Bülles
• Thorsten Beckmann
• Georg Linden
• Annika Kiefner
• Pascal Beyer
• Kevin Li