Fiber products of elliptic surfaces with section and associated Kummer fibrations

2008/02/26 by Kapustka, Grzegorz, Grzegorz Kapustka, Michal Kapustka +1 · 2 citations
Mathematics · #14J27 #14J32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.AG #msc:14J27 #msc:14J32

paper · pdf · doi:10.48550/arxiv.0802.3760

To appear in Internat. J. Math. 23 pages

arxiv created 2008/02/26 · openalex publication_date 2008/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find formulas to compute the Hodge numbers of obtained three folds in terms of the types of singular fibers of the elliptic surfaces. Next we study Kummer fibrations associated to these fiber products.

Cited by

• Periods of fibre products of elliptic surfaces and the Gamma conjecture
• Correspondences between modular Calabi--Yau fiber products

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• Correspondences between modular Calabi--Yau fiber products
• Compact moduli of elliptic surfaces with a multiple fiber
• New families of Calabi-Yau 3-folds without maximal unipotent monodromy
• Calabi--Yau 3-folds of Borcea--Voisin type and elliptic fibrations
• On the motive of Kummer varieties associated to Γ₁(7) - Supplement to the paper: The modularity of certain non-rigid Calabi-Yau threefolds (by R. Livné and N. Yui)