A projective log Calabi–Yau surface with reduced boundary, ample boundary support and a G_m-action is exactly a tropical mutation surface with a single shear, and its complexity equals the number of distinct roots of f.
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Geometry of tropical mutation surfaces with a single mutation
A projective log Calabi–Yau surface with reduced boundary, ample boundary support and a G_m-action is exactly a tropical mutation surface with a single shear, and its complexity equals the number of distinct roots of f.