Degenerations of del Pezzo surfaces I
Abstract
Let X be a surface with quotient singularities which admits a smoothing to the plane. We prove that X is a deformation of a weighted projective plane P(a2,b2,c2), where a,b,c is a solution of the Markov equation a2+b2+c2=3abc. We also prove a generalisation for del Pezzo surfaces of degree K2 at least 5.
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