K3 Surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers

[摘要] We classify complex K3 surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers. These surfaces are characterized by the fact that they admit a unique elliptic fibration with infinite automorphism group. We furnish an explicit list of 32 Neron-Severi lattices corresponding to such surfaces. Incidentally, we are able to decide which of these 32 classes of surfaces admit a unique elliptic pencil. Finally, we prove that all K3 surfaces with Picard rank >= 19 and infinite automorphism group have positive entropy. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] K3 surfaces;Automorphisms;Elliptic fibrations;Lattices