Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves

Abstract

We study threefolds fibred by Kummer surfaces associated to products of elliptic curves, that arise as resolved quotients of threefolds fibred by certain lattice polarized K3 surfaces under a fibrewise Nikulin involution. We present a general construction for such surfaces, before specializing our results to study Calabi-Yau threefolds arising as resolved quotients of threefolds fibred by mirror quartic K3 surfaces. Finally, we give some geometric properties of the Calabi-Yau threefolds that we have constructed, including expressions for Hodge numbers.

v2: Minor corrections, references updated. Final version, accepted for publication in String-Math 2014, forthcoming volume in the Proceedings of Symposia in Pure Mathematics series

References in corpus (2)

• Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
• Fiber products of elliptic surfaces with section and associated Kummer fibrations

Cited by in corpus (5)

• Weighted Hurwitz numbers and topological recursion: an overview
• Rationally weighted Hurwitz numbers, Meijer $G$-functions and matrix integrals
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Hodge Numbers from Picard-Fuchs Equations
• Threefolds Fibred by Mirror Sextic Double Planes