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Hodge Theory with Applications
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Professor
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Prof. Brent Doran
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Assistants
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Patrik Hubschmid (Seminar), Jun Yu (Exercises)
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Place
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HG G 26.3 (Seminar) / HG F 26.3 (Exercises)
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Time
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Friday 15:30-17:15 for the seminar and Friday 09:15-10:00 for the exercises
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Beginning
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Friday, 08.10.2010, 15:30-17:15 (seminar)
Friday, 15.10.2010, 09:15-10:00 (exercises)
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Prerequisites
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Complex analysis (Funktionentheorie), Algebra I + II, some knowledge about differential geometry is an advantage
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Description
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The seminar gives an introduction to Hodge theory of Kähler varieties following the first four parts of the book of Claire Voisin.
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Literature
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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.
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Further information
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Each speaker will assign two problems to the audience which will be discussed one week later.
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Testat requirement
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Give a talk and submit one third of the exercises
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Exercise sheets
Schedule
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Date
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Title
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Speaker(s)
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08.10.2010
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Chapter 1: Holomorphic functions of several variables
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Marco Cincera
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15.10.2010
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Chapter 2: Complex manifolds
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Mark Hannay, Oliver Sonderegger
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22.10.2010
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Chapter 3: Kähler metrics
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Reto Bütler, Carl Vollenweider
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29.10.2010
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Chapter 5: Harmonic forms and cohomology
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Reto Häberli
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05.11.2010
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Chapter 6: The case of Kähler manifolds
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Gian Hail
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12.11.2010
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Chapter 4: Sheaves and cohomology
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Dimitri Wyss
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19.11.2010 / 26.11.2010
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Chapter 7: Hodge structures and polarisations
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Hiep Pham Duc / Bledar Fazlija
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26.11.2010
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Chapter 8: Holomorphic de Rham complexes and spectral sequences
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Andreas Steiger
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03.12.2010
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Chapter 9: Families and deformations
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Maël Pavon
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10.12.2010
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Chapter 10: Variations of Hodge structure
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Daniel Würsch
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17.12.2010
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Chapter 11: Hodge classes
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Claudio Sibilia
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