Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds

2009/11/02 by Pedro Luis del Angel, Stefan Müller–Stach, del Angel, Pedro Luis +5
Mathematics · #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0911.0277

openalex publication_date 2009/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use L²-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H¹( S, j_*\V), where the local system \V arises from the third primitive cohomology of family of Calabi-Yau threefolds over a curve S. The method gives a way to predict the presence of algebraic 2-cycles in the total space of the family and is applied to some examples.

Citations

• Tables of Calabi--Yau equations

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