Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part. (English) Zbl 0770.14003

André, Yves

Compos. Math. 82, No. 1, 1-24 (1992).

The paper offers the following group-theoretic interpretation of the theorem of the fixed part of Steenbrink-Zucker [cf. J. Steenbrink and S. Zucker, Invent. Math. 80, 489-542 (1985; Zbl 0626.14007)]. For almost all stalks of a polarisable good variation of mixed Hodge structure the connected monodromy group is a normal subgroup of the derived Mumford-Tate group. Then the “size” of the quotient group is studied. Applications are given to the algebraic independence of abelian integrals.

Reviewer: A.Buium (Bucureşti)

MSC:

14D07	Variation of Hodge structures (algebro-geometric aspects)
14C30	Transcendental methods, Hodge theory (algebro-geometric aspects)

Keywords:

theorem of the fixed part; variation of mixed Hodge structure; Mumford- Tate group; abelian integrals

Citations:

Zbl 0626.14007

References:

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