On the uniqueness of elliptic K3 surfaces with maximal singular fibre
Annales de l'Institut Fourier, Volume 63 (2013) no. 2, p. 689-713

We explicitly determine the elliptic K3 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.

Nous déterminons des équations explicites pour les surfaces elliptiques de type K3 qui ont une section et une fibre singulière maximale. Si la caractéristique du corps sous-jacent est différente de 2, pour chacun des deux types de fibre maximale, I 19 et I 14 * , la surface est unique. En caractéristique 2 les fibres maximales sont de type I 18 ou I 13 * , et il y a deux, respectivement une, familles 1-dimensionales de telles surfaces.

DOI : https://doi.org/10.5802/aif.2773
Classification:  14J27,  14J28,  11G05
Keywords: elliptic surface, K3 surface, maximal singular fibre, wild ramification.
@article{AIF_2013__63_2_689_0,
     author = {Sch\"utt, Matthias and Schweizer, Andreas},
     title = {On the uniqueness of elliptic K3 surfaces with maximal singular fibre},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {2},
     year = {2013},
     pages = {689-713},
     doi = {10.5802/aif.2773},
     mrnumber = {3112845},
     zbl = {1273.14078},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2013__63_2_689_0}
}
Schütt, Matthias; Schweizer, Andreas. On the uniqueness of elliptic K3 surfaces with maximal singular fibre. Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 689-713. doi : 10.5802/aif.2773. http://www.numdam.org/item/AIF_2013__63_2_689_0/

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