Automorphisms of certain Niemeier lattices and Elliptic Fibrations

2016/09/14 by Marie José Bertin, Bertin, Marie José, Odile Lecacheux +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1609.04154

openalex publication_date 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 53th fibration, thanks to a remark of Elkies and Schütt. We characterize the fibration both theoretically and with a Weierstrass model.

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