The maximal singular fibres of elliptic K3 surfaces
نویسنده
چکیده
We prove that the maximal singular fibres of elliptic K3 surfaces have type I19 and I∗ 14 unless the characteristic of the ground field is 2. In characteristic 2, the maximal singular fibres are I18 and I ∗ 13. The paper supplements work of Shioda in [9] and [10]. MSC (2000): 11G25, 14J27, 14J28.
منابع مشابه
Arithmetic of the [19,1,1,1,1,1] Fibration
Suppose π : S → P is an elliptic K3-surface over C with a section, such that all its singular fibres are multiplicative. Suppose moreover that π is extremal, i.e., the group of sections of π is finite and the rank ρ of the Néron-Severi group NS(S) of S is maximal, so ρ = 20. A formula of Shioda and Tate [Sh90, Cor. 5.3] then implies that π has precisely 6 singular fibers, consisting of ni compo...
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