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 [20]. We then specialize our construction to the context of [6], 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.
Variations of mixed Hodge structure, Higgs fields, and quantum cohomology
Pearlstein G. J.
Co-primo
2000-01-01
Abstract
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 [20]. We then specialize our construction to the context of [6], 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.File in questo prodotto:
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