On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Abstract

We explicitly determine the elliptic K3 surfaces with a maximal singular fibre. If the characteristic of the ground field is different from 2, for each of the two possible maximal fibre types, $I_{19}$ and $I_{14}^{\ast }$, the surface is unique. In characteristic 2 the maximal fibre types are $I_{18}$ and $I_{13}^{\ast }$, and there exist two (resp. one) one-parameter families of such surfaces.

20 pages; v2: refereed version with some corrections and additions; author addresses and bibliography updated

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