Department of Mathematics

Hodge Theory with Applications

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Professor Prof. Brent Doran
Assistants Patrik Hubschmid (Seminar), Jun Yu (Exercises)
Place HG G 26.3 (Seminar) / HG F 26.3 (Exercises)
Time Friday 15:30-17:15 for the seminar and Friday 09:15-10:00 for the exercises
Beginning Friday, 08.10.2010, 15:30-17:15 (seminar)
Friday, 15.10.2010, 09:15-10:00 (exercises)
Prerequisites Complex analysis (Funktionentheorie), Algebra I + II, some knowledge about differential geometry is an advantage
Description The seminar gives an introduction to Hodge theory of Kähler varieties following the first four parts of the book of Claire Voisin.
Literature Claire Voisin, Hodge theory and complex algebraic geometry, Cambridge studies in advanced mathematics, 2002-2003.
Phillip Griffiths, Joseph Harris, Principles of algebraic geometry, Wiley, 1994.
Further information Each speaker will assign two problems to the audience which will be discussed one week later.
Testat requirement Give a talk and submit one third of the exercises

Exercise sheets

Exercise sheet as pdf file Due date Solution (only selected exercises)
Chapter 1 October 15, 2010 Solution 1
Chapter 2 October 22, 2010 Solution 2
Chapter 3 October 29, 2010 Solution of Ex. 2
Chapter 5 November 5, 2010  
Chapter 6 November 12, 2010 Solution of Ex. 1
Chapter 4 November 19, 2010  
Chapter 8 December 3, 2010  
Chapter 7 December 10, 2010  
Chapters 9 and 10 December 17, 2010 Solution of Ex. 2
Chapter 11 optional  


Date Title Speaker(s)
08.10.2010 Chapter 1: Holomorphic functions of several variables Marco Cincera
15.10.2010 Chapter 2: Complex manifolds Mark Hannay, Oliver Sonderegger
22.10.2010 Chapter 3: Kähler metrics Reto Bütler, Carl Vollenweider
29.10.2010 Chapter 5: Harmonic forms and cohomology Reto Häberli
05.11.2010 Chapter 6: The case of Kähler manifolds Gian Hail
12.11.2010 Chapter 4: Sheaves and cohomology Dimitri Wyss
19.11.2010 / 26.11.2010 Chapter 7: Hodge structures and polarisations Hiep Pham Duc / Bledar Fazlija
26.11.2010 Chapter 8: Holomorphic de Rham complexes and spectral sequences Andreas Steiger
03.12.2010 Chapter 9: Families and deformations Maël Pavon
10.12.2010 Chapter 10: Variations of Hodge structure Daniel Würsch
17.12.2010 Chapter 11: Hodge classes Claudio Sibilia

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