Degenerations of del Pezzo surfaces I

Paul Hacking; Yuri Prokhorov

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Degenerations of del Pezzo surfaces I

Paul Hacking·Yuri Prokhorov

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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(a^2,b^2,c^2), where a,b,c is a solution of the Markov equation a^2+b^2+c^2=3abc. We also prove a generalisation for del Pezzo surfaces of degree K^2 at least 5.

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Paul Hacking, Yuri Prokhorov. 2005-09-22. Degenerations of del Pezzo surfaces I. https://arxiv.org/abs/math/0509529

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