Variations of mixed Hodge structure, Higgs fields, and quantum cohomology
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Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural Higgs bundle structure ∂ + θ which is invariant under the ℂ* action studied in . We then specialize our construction to the context of , and show that the resulting Higgs field θ determines (and is determined by) the Gromov-Witten potential of the underlying family of Calabi-Yau threefolds.
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