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On the uniqueness of elliptic K3 surfaces with maximal singular fibre

Matthias SchüttAndreas Schweizer — 2013

Annales de l’institut Fourier

We explicitly determine the elliptic K 3 surfaces with section and 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 * , the surface is unique. In characteristic 2 the maximal fibre types are I 18 and I 13 * , and there exist two (resp. one) one-parameter families of such surfaces.

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