Degenerations of del Pezzo surfaces I

Details Degenerations of del Pezzo surfaces I Degenerations of del Pezzo surfaces I

2005-09-22

arxiv.org/abs/math/0509529v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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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