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

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.

### MSC:

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

Zbl 0626.14007
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### References:

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