VARIATION OF MIXED HODGE STRUCTURES

Patrick Brosnan (1) , Fouad Elzein (2)

1 ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
2 IMJ - Institut de Mathématiques de Jussieu

Variation of mixed Hodge structures(VMHS), introduced by P. Deligne, is a linear structure reflecting the geometry on cohomology of the fibers of an algebraic family, generalizing variation of Hodge structures for smooth proper families, introduced by P. Griffiths. Hence, it is a strong tool to study the variation of the geometric structure of fibers of a morphism. We describe here the degenerating properties of a VMHS of geometric origin and the existence of a relative monodromy filtration, as well the definition and properties of abstract admissible VMHS.

Mots clés: Hodge theory; algebraic geometry; Mixed Hodge structure.; Mixed Hodge structure

Domaines: Géométrie algébrique [math.AG]

Patrick Brosnan, Fouad Elzein. VARIATION OF MIXED HODGE STRUCTURES. 2012. ⟨hal-00793746⟩