The Gauss–manin Connection on the Hodge Structures
نویسنده
چکیده
The Gauß–Manin connection is an extra structure on the de Rham cohomology of any algebraic variety, ∇ : H dR/k −→ Ωk ⊗k H dR/k (its definition will appear below). If one believes the Hodge conjecture then for a given pure Hodge structure H there is at most one connection ∇ such that H is a Hodge substructure of a cohomology group of a smooth projective complex variety with ∇ induced by the Gauß–Manin connection. Independently of the Hodge conjecture, there are at most countably many connections ∇ on a given pure Hodge structure H such that H is a Hodge substructure of a cohomology group of a smooth projective complex variety with ∇ induced by the Gauß–Manin connection (cf. Corollary 2.4). The original motivation for this paper were the properties of the forgetful functor
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