Cylinders in singular del Pezzo surfaces

Ivan Cheltsov; Jihun Park; Joonyeong Won

doi:10.1112/S0010437X16007284

Cylinders in singular del Pezzo surfaces

Ivan Cheltsov, Jihun Park, Joonyeong Won

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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 Q-divisor D that is Q-linearly equivalent to -K_Sand 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 G_a-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	https://doi.org/10.1112/S0010437X16007284
State	Published - 1 Jun 2016

Bibliographical note

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

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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.",

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AU - Cheltsov, Ivan

AU - Park, Jihun

AU - Won, Joonyeong

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N2 - 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.

AB - 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.

KW - G -action

KW - affine cone

KW - anticanonical divisor

KW - cylinder

KW - del Pezzo surface

KW - du Val singularity

KW - log canonical singularity

KW - minimal resolution

KW - weak del Pezzo surface

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VL - 152

SP - 1198

EP - 1224

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 6

ER -

Cylinders in singular del Pezzo surfaces

Abstract

Bibliographical note

Keywords

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