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arXiv · 1912.08583

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

Giacomo Mezzedimi
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Abstract

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 N\'eron-Severi lattices corresponding to such surfaces. Incidentally, we are able to decide which of these 32 classes of surfaces admit a unique genus 1 fibration. Finally, we prove that all K3 surfaces with Picard rank >=19 and infinite automorphism group have positive entropy.

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Giacomo Mezzedimi. 2019-12-18. K3 Surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers. https://arxiv.org/abs/1912.08583

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