Finiteness of Néron-Severi lattices for K3 surfaces with non-elementary hyperbolic automorphism groups, with explicit descriptions, when Picard number ≥6.
On K3 surfaces with hyperbolic automorphism groups
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abstract
We show the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.
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On K3 surfaces with hyperbolic automorphism groups
Finiteness of Néron-Severi lattices for K3 surfaces with non-elementary hyperbolic automorphism groups, with explicit descriptions, when Picard number ≥6.