Elliptic fibrations and involutions on K3 surfaces

2023/04/03 by Alice Garbagnati, Cecília Salgado, Garbagnati, Alice +1
Mathematics · #14J26 #14J27 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2304.01383

openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey our contributions on the classification of elliptic fibrations on K3 surfaces with a non-symplectic involution. We place them in the more general framework of K3 surfaces with an involution without any hypothesis on its fixed locus or on the action on the symplectic 2-form. We revisit the complete classification of elliptic fibrations on K3 surfaces with a 2-elementary Néron--Severi lattice, and give a complete classification of extremal elliptic fibrations on K3 surfaces that are quadratic covers of rational elliptic surfaces.

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