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Cylinders in singular del Pezzo surfaces
Published online by Cambridge University Press: 21 April 2016
Abstract
For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a
$(-K_{S})$-polar cylinder or not. If it allows one, then we present an effective
$\mathbb{Q}$-divisor
$D$ that is
$\mathbb{Q}$-linearly equivalent to
$-K_{S}$ and such that the open set
$S\setminus \text{Supp}(D)$ is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial
$\mathbb{G}_{a}$-actions on their affine cones defined by their anticanonical divisors.
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- Research Article
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- Copyright
- © The Authors 2016
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