Abstract
Let C be a regular geometrically integral curve over an imperfect field K and assume that it admits a non-smooth point p which — seen as a prime of the separable function field K(C)|K — is non-decomposed in the base field extension K‾⊗KK(C)|K‾. In this paper we establish a bound for the number of iterated Frobenius pullbacks needed in order to transform p into a rational point. This provides an algorithm to compute geometric δ-invariants of non-smooth points and a procedure to construct fibrations with moving singularities of prescribed δ-invariants. We show that the bound is sharp in characteristic 2. We further study the geometry of a pencil of plane projective rational quartics in characteristic 2 whose generic fibre attains our bound. On our way, we prove several results on separable and non-decomposed points that might be of independent interest.
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