This is the website for the seminar on Hodge theory held at the Johannes-Gutenberg University of Mainz during the Summersemester of 2015.
Organizers: Ana-Maria Brecan, Ariyan Javanpeykar, Ronan Terpereau
Schedule: Thursday 10h00-12h00 in Room 04-432
- 30th April. Hodge decomposition of a variety I. Markus
Content: Voisin I, Chapter II.5
- 7th May. Hodge decomposition of a variety II. Timo
Content: Voisin, Chapter II.6
- 14th May. No talk
- 21st May. Examples of Hodge decompositions. Ronan
Content: Curves, abelian varieties, hypersurfaces, K3 surfaces, Enriques surfaces, surfaces of Hodge level zero, double covers of Pn, Calabi-Yau manifolds. Computing hodge numbers and determining period domains.
- 28th May. Global Torelli for K3 surfaces. Carolin
- 3rd June. No talk
- 11th June. Jacobian rings and applications. Stefan
- 18th June. Monodromy representations. Bernd
Content: Start with elliptic curves as in Chapter 1.1 "Period mappings " and then do Lefschetz pencils as in Voisin II Chapter 1.3
- 25th June. Period domains. Ana
Content: Polarized Hodge structures, Flag varieties, Real group orbits, Complex flag manifolds, Mumford-Tate domains
- 2nd July. Period maps. Ana & Pavel
Content: Voisin I Chapter III.10
- 9th July. Griffiths transversality and Gauss-Manin connection. Pavel
Content: Voisin I, Chapter III.9.2
- 16th July. No talk.
- 23rd July. The infinitesimal Torelli theorem for CY manifolds, non-hyperelliptic curves and hypersurfaces. Ariyan (TBC)
Content: Voisin I, Chapter 10.3
- Period mappings and Period domains. J. Carlson, C. Peters and S. Mueller-Stach.
- Voisin http://www.math.columbia.edu/~thaddeus/seattle/voisin.pdf
- Voisin Hodge Theory and Complex Algebraic Geometry I & II
- Edixhoven http://pub.math.leidenuniv.nl/~edixhovensj/talks/2012/2012_06_shimura.pdf
- Milne http://www.jmilne.org/math/xnotes/svh.pdf
- Huybrechts http://www.math.uni-bonn.de/people/huybrech/K3Global.pdf
- Griffiths, Harris: Principles of Algebraic geometry
- Demailly: https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
- Peters Steenbrink: Mixed Hodge Structures