Smoothable del Pezzo surfaces with quotient singularities

Details Smoothable del Pezzo surfaces with quotient singularities Smoothable del Pezzo surfaces with quotient singularities

2008-08-11

arxiv.org/abs/0808.1550v2

Compositio Math. 146 (2010), 169-192

Mathematics

Algebraic Geometry

36 pages. v2: corrected attribution of Prop. 2.7, added reference

Scientific paper

We give a complete classification of del Pezzo surfaces with quotient singularities and Picard rank 1 which admit a Q-Gorenstein smoothing. There are 14 infinite families of toric examples. The surfaces in each family correspond to solutions of a Markov-type equation. The remaining surfaces are obtained as deformations of the toric surfaces or belong to a finite list of sporadic surfaces.

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