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arXiv · 1609.04154

Automorphisms of certain Niemeier lattices and Elliptic Fibrations

Marie José Bertin·Odile Lecacheux
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Abstract

Nishiyama introduced a lattice theoretic classification of the elliptic fibrations on a $K3$ surface. In a previous paper we used his method to exhibit $52$ elliptic fibrations, up to isomorphisms, of the singular $K3$ surface of discriminant $-12$. We prove here that the list is complete with a $53$th fibration, thanks to a remark of Elkies and Sch\"{u}tt. We characterize the fibration both theoretically and with a Weierstrass model.

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Marie José Bertin, Odile Lecacheux. 2016-09-14. Automorphisms of certain Niemeier lattices and Elliptic Fibrations. https://arxiv.org/abs/1609.04154

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