On Néron–Severi lattices of Jacobian elliptic K3 surfaces

We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell–Weil group on K3 surfaces with infinite automorphism group and 2-elementary Néron–Severi lattice. As part of the classification, we comput...

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Published in:Manuscripta mathematica 2024-03, Vol.173 (3-4), p.847-866
Main Authors: Clingher, Adrian, Malmendier, Andreas
Format: Article
Language:English
Subjects:
Algebraic Geometry
Automorphisms
Calculus of Variations and Optimal Control
Optimization
Classification
Geometry
Lattices
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Malmendier, Andreas
description We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell–Weil group on K3 surfaces with infinite automorphism group and 2-elementary Néron–Severi lattice. As part of the classification, we compute the lattice theoretic multiplicities of all Jacobian elliptic fibrations in both cases.
doi_str_mv 10.1007/s00229-023-01486-3
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subjects Algebraic Geometry
Automorphisms
Calculus of Variations and Optimal Control
Optimization
Classification
Geometry
Lattices
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
title On Néron–Severi lattices of Jacobian elliptic K3 surfaces
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