English

Smoothable del Pezzo surfaces with quotient singularities

Algebraic Geometry 2019-02-20 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0808.1550,
  title  = {Smoothable del Pezzo surfaces with quotient singularities},
  author = {Paul Hacking and Yuri Prokhorov},
  journal= {arXiv preprint arXiv:0808.1550},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-21T11:09:27.007Z