Hodge numbers from picard–fuchs equations

Charles F. Doran, Andrew Harder, Alan Thompson

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Given a variation of Hodge structure over P1 with Hodge numbers (1, 1,…, 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds.

Original languageEnglish (US)
Article number045
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume13
DOIs
StatePublished - Jun 18 2017

Keywords

  • Calabi
  • Variation of hodge structures
  • Yau manifolds

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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