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manuscripta mathematica

, Volume 102, Issue 3, pp 269–310 | Cite as

Variations of mixed Hodge structure, Higgs fields, and quantum cohomology

  • Gregory J. Pearlstein

Abstract:

Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural Higgs bundle structure \(\) 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.

Mathematics Subject Classification (2000): 14D07, 32G20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gregory J. Pearlstein
    • 1
  1. 1.University of California Santa Cruz, Santa Cruz, CA 95064, USA.¶e-mail: gpearl@math.ucsc.eduUS

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