Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1198-1224 |
| Number of pages | 27 |
| Journal | Compositio Mathematica |
| Volume | 152 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1 Jun 2016 |
Bibliographical note
Funding Information:The authors would like to express their sincere appreciation to the referee for the invaluable comments. The referee's comments enabled the authors to improve their results as well as their exposition. The rst author was supported within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program. The second author has been supported by IBS-R003-D1, Institute for Basic Science in Korea. The third author has been supported by NRF-2014R1A1A2056432 and NRF-2007-0056093 (ASARC), the National Research Foundation in Korea.
Publisher Copyright:
© 2016 The Authors.
Keywords
- G -action
- affine cone
- anticanonical divisor
- cylinder
- del Pezzo surface
- du Val singularity
- log canonical singularity
- minimal resolution
- weak del Pezzo surface