Transcendental lattices of certain singular K3 surfaces

2021/12/17 by Marie José Bertin, Bertin, Marie José, Odile Lecacheux +1
Mathematics · #11F23 #11G05 #14J27 (Secondary) #14J28 (Primary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2112.09592

openalex publication_date 2021/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the transcendental lattices of the singular K3 surfaces belonging to three pencils of K3 surfaces, namely the Apéry-Fermi pencil with transcendental lattice U⊕ ⟨ 12 ⟩, the Verrill's pencil with transcendental lattice U ⊕ ⟨ 6 ⟩ and another pencil linked to Verrill's pencil with transcendental lattice U ⊕ ⟨ 24 ⟩. Many corollaries are deduced. For example, some singular K3 surfaces belong to different pencils or are Kummer surfaces of K3 surfaces of another pencil.

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