Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces

Abstract

We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the moduli space of mirror quartic K3 surfaces. This is then used to give a complete explicit description of all Calabi-Yau threefolds fibred by mirror quartic K3 surfaces. We conclude by studying the properties of such Calabi-Yau threefolds, including their Hodge numbers and deformation theory.

v2: Significant changes at the request of the referee. Section 3 has been rearranged to accommodate a revised proof of Proposition 3.5 (formerly 3.2). Section 5 has been removed completely, it will instead appear as part of Section 5 in arxiv:1601.08110

References in corpus (4)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Supersymmetric partition functions on Riemann surfaces
• Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds

Cited by in corpus (8)

• Supersymmetric partition functions on Riemann surfaces
• Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces
• Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves
• Hodge Numbers from Picard-Fuchs Equations
• Threefolds Fibred by Mirror Sextic Double Planes
• The Doran-Harder-Thompson conjecture for toric complete intersections
• Modularity of Landau-Ginzburg models
• The Mirror Clemens-Schmid Sequence