The 14th case VHS via K3 fibrations

Abstract

We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our attention to these families is motivated by the Doran-Morgan classification of variations of Hodge structure which can underlie families of Calabi-Yau threefolds with $h^{2,1}=1$ over the thrice-punctured sphere. We explore their torically induced fibrations by $M$-polarized K3 surfaces and use these fibrations to construct an explicit geometric transition between an anticanonical hypersurface and a nef complete intersection through a singular subfamily of hypersurfaces. Moreover, we show that another singular subfamily provides a geometric realization of the missing "14th case" variation of Hodge structure from the Doran-Morgan list.

References in corpus (3)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Lattice polarized toric K3 surfaces
• Families of lattice polarized K3 surfaces with monodromy

Cited by in corpus (6)

• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Supercongruences for rigid hypergeometric Calabi--Yau threefolds
• Families of lattice polarized K3 surfaces with monodromy
• Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves
• The Doran-Harder-Thompson conjecture for toric complete intersections
• Two One-Parameter Special Geometries