Cylinders in singular del Pezzo surfaces

Ivan Cheltsov, Jihun Park, Joonyeong Won

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


For each del Pezzo surface S with du Val singularities, we determine whether it admits a (-KS)-polar cylinder or not. If it allows one, then we present an effective Q-divisor D that is Q-linearly equivalent to -KSand such that the open set S\Supp(D) is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial Ga-actions on their affine cones defined by their anticanonical divisors.

Original languageEnglish
Pages (from-to)1198-1224
Number of pages27
JournalCompositio Mathematica
Issue number6
StatePublished - 1 Jun 2016


  • G -action
  • affine cone
  • anticanonical divisor
  • cylinder
  • del Pezzo surface
  • du Val singularity
  • log canonical singularity
  • minimal resolution
  • weak del Pezzo surface


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