Elliptic and K3 fibrations on double octic Calabi-Yau threefolds

2025/04/14 by Sławomir Cynk, Cynk, Sławomir, Beata Kocel-Cynk +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2504.10759

openalex publication_date 2025/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fibrations by elliptic curves and K3 surfaces of double octic Calabi-Yau threefolds determined by singular lines and points of multiplicity at least 4 of the defining octic arrangement. As a consequence we conclude that every double octic admits many elliptic and K3 fibrations. We apply descriptions of some K3 fibrations to construct a birational map between elements of two families of double octics.

Citations

• Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds
• Boundedness of elliptic Calabi-Yau threefolds
• Elliptic threefolds with high Mordell-Weil rank
• A special Calabi-Yau degeneration with trivial monodromy
• Hilbert modularity of some double octic Calabi--Yau threefolds
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Picard-Fuchs operators for octic arrangements I (The case of orphans)
• Classification of double octic Calabi-Yau threefolds
• 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Quantum geometry of elliptic Calabi-Yau manifolds
• Small Resolutions and Non-Liftable Calabi-Yau threefolds
• Modular Calabi-Yau threefolds of level eight

Related

• Double covers of P³ and Calabi-Yau varieties
• Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds
• Linear systems on rational elliptic surfaces and elliptic fibrations on K3 surfaces
• Families of Calabi-Yau elliptic fibrations in ℙ(L^a ⊕ L^b ⊕ O_B)
• Classification of all Jacobian elliptic fibrations on certain K3 surfaces