Christophe Mourougane

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Cours doctoral Structures de Hodge mixtes Mixed Hodge structures

I will first present the definition and some examples of mixed Hodge structures.
I will then display, on the example of degenerations of projective varieties,
the existence of weight structures and their compatibility with geometric morphisms.
This provides a great deal of information on the singularities of the special fiber.
On the way, I will recall cohomological methods like spectral sequences associated to filtration of sheaves.


"Hodge theory" Fouad El Zein, Fouad; Lê Dũng Tráng .
Hodge theory, pages 123–216, Math. Notes, Volume 49, Princeton Univ. Press, Princeton, NJ, 2014

"The Clemens-Schmid exact sequence and applications" David R. Morrison,
Topics in transcendental algebraic geometry, Ann. of Math. Stud.,
volume 106, pages 101--119. Princeton Univ. Press, Princeton, NJ, 1984.

"Mixed Hodge Structures" Chris A.M. Peters  et Joseph H.M. Steenbrink 
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
A Series of Modern Surveys in Mathematics book series (MATHE3, volume 52)

A naive guide to mixed Hodge theory Alan H. Durfee
Proceeddings of Symposis in Pure Mathematics / Volume 40 (1983) Part 1, 313-320.

Théorie de Hodge et géométrie algébrique complexe Claire Voisin
Cours spécialisés de la SMF, Volume 10, (2002).

Premier cours : Structures de Hodge
Deuxième cours : Structures de Hodge mixtes vendredi 12 février à 10h15 dans l'Amphi Lebesgue (IRMAR)
Troisième cours : Suite de Clemens-Schmid jeudi 18 février à 10h15 dans la salle 16 (IRMAR)