Torelli theorems and Hodge theory

This is the website for the seminar on Hodge theory held at the Johannes-Gutenberg University of Mainz during the Summersemester of 2015.


Practical information


Organizers: Ana-Maria Brecan, Ariyan Javanpeykar, Ronan Terpereau

Schedule:  Thursday 10h00-12h00 in Room 04-432




  1. 30th April.  Hodge decomposition of a variety I. Markus
    Content: Voisin I, Chapter II.5
  2. 7th May.  Hodge decomposition of a variety II. Timo
    Voisin, Chapter II.6
  3. 14th May. No talk
  4. 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.
  5. 28th May.  Global Torelli for K3 surfaces.  Carolin
  6. 3rd June. No talk
  7. 11th June. Jacobian rings and applications. Stefan
  8. 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
  9. 25th June. Period domains. Ana
    Content: Polarized Hodge structures, Flag varieties, Real group orbits, Complex flag manifolds, Mumford-Tate domains
  10. 2nd July. Period maps. Ana & Pavel
    Content: Voisin I Chapter III.10
  11. 9th July.  Griffiths transversality and Gauss-Manin connection. Pavel
    Content: Voisin I, Chapter III.9.2
  12. 16th July.  No talk.
  13. 23rd July.  The infinitesimal Torelli theorem for CY manifolds, non-hyperelliptic curves and hypersurfaces. Ariyan (TBC)
    Content: Voisin I, Chapter 10.3




  1. Period mappings and Period domains. J. Carlson, C. Peters and S. Mueller-Stach.
  2. Voisin
  3. Voisin Hodge Theory and Complex Algebraic Geometry I & II
  4. Edixhoven
  5. Milne
  6. Huybrechts
  7. Griffiths, Harris: Principles of Algebraic geometry
  8. Demailly:
  9. Peters Steenbrink: Mixed Hodge Structures