For k-forms of blow-ups of P(1,1,m), rationality and cylindricity are determined, in the covered cases, by the blow-up count n, the Galois-orbit invariant ℓ_S, and the k-points of the exceptional curve Q.
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Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero
For k-forms of blow-ups of P(1,1,m), rationality and cylindricity are determined, in the covered cases, by the blow-up count n, the Galois-orbit invariant ℓ_S, and the k-points of the exceptional curve Q.