Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3

2024/03/15 by Meira, Felipe Zingali
#14J27 (Primary) 14J28 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.10712

Abstract

We classify Jacobian elliptic fibrations on K3 surfaces with a non-symplectic automorphism σ of order 3 according to the action of σ on their fibres, building on work by Garbagnati and Salgado for non-symplectic involutions. We determine the possible reducible fibres types and give Weierstrass equations for Jacobian elliptic fibration which are preserved by σ. For a K3 surface X with Picard number at least 12 and σ acting trivially on \NS X, we apply the Kneser--Nishiyama method to find its Jacobian elliptic fibrations, and use our method to classify them in relation to every non-symplectic automorphism of order 3 in \Aut X.

Related

• Elliptic fibrations and involutions on K3 surfaces
• Elliptic fibrations on K3 surfaces with a non-symplectic involution fixing rational curves and a curve of positive genus
• On two-elementary K3 surfaces with finite automorphism group
• Automorphisms of certain Niemeier lattices and Elliptic Fibrations
• Jacobian fibrations on the singular K3 surface of discriminant 3