Mixed twistor structures

Details Mixed twistor structures Mixed twistor structures

1997-05-05

arxiv.org/abs/alg-geom/9705006v1

Mathematics

Algebraic Geometry

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Scientific paper

The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory of weights for various things surrounding arbitrary representations of the fundamental group of a smooth projective variety. We give some examples of generalizations of classical results for variations of mixed Hodge structure, to the twistor setting. This supports a ``meta-theorem'' (which we state but don't prove) that one can everywhere replace the word ``Hodge'' by the word ``twistor''. We show that the jet spaces of hyperk\"ahler or more generally hypercomplex manifolds have natural mixed twistor structures which determine the hypercomplex structure in a formal neighborhood of a point.

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