Variation Of Mixed Hodge Structures

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.