Finiteness of Néron-Severi lattices for K3 surfaces with non-elementary hyperbolic automorphism groups, with explicit descriptions, when Picard number ≥6.
Geometrical finiteness for automorphism groups via cone conjecture
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abstract
This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties. As an application, it follows that such groups are non-positively curved: relatively hyperbolic and ${\rm CAT(0)}$. In the case of K3 surfaces, we clarify the relationship between Kleinian lattices and $(-2)$-curves, and between convex-cocompact Kleinian groups and genus-one fibrations.
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UNVERDICTED 2representative citing papers
Gap theorems are proved for entropy norms of automorphisms on K3, Enriques, and IHS manifolds, with achirality characterized using genus-one fibrations.
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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.
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Gap theorems and achirality for automorphisms of K3 surfaces and Enriques surfaces
Gap theorems are proved for entropy norms of automorphisms on K3, Enriques, and IHS manifolds, with achirality characterized using genus-one fibrations.