no. 2
On the uniqueness of elliptic K3 surfaces with maximal singular fibre
[Sur l’unicité des surfaces elliptiques de type K3 ayant une fibre singulière maximale]
Schütt, Matthias1 ; Schweizer, Andreas2
1 Institut für Algebraische Geometrie Leibniz Universität Hannover Welfengarten 1 30167 Hannover Germany
2 Department of Mathematics Korea Advanced Institute of Science and Technology (KAIST) Daejeon 305-701 South Korea
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 689-713.

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.

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.

DOI : 10.5802/aif.2773
Classification : 14J27, 14J28, 11G05
Keywords: elliptic surface, $K3$ surface, maximal singular fibre, wild ramification.
Mots-clés : surface elliptique, surface de type $K3$, fibre singulière maximale, ramification sauvage

Schütt, Matthias 1 ; Schweizer, Andreas 2

1 Institut für Algebraische Geometrie Leibniz Universität Hannover Welfengarten 1 30167 Hannover Germany
2 Department of Mathematics Korea Advanced Institute of Science and Technology (KAIST) Daejeon 305-701 South Korea 
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Schütt, Matthias; Schweizer, Andreas. On the uniqueness of elliptic K3 surfaces with maximal singular fibre. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 689-713. doi : 10.5802/aif.2773. https://aif.centre-mersenne.org/articles/10.5802/aif.2773/

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