Cylinders in del Pezzo surfaces with du Val singularities

Grigory Belousov

doi:10.4134/BKMS.b160684

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(5): 1655-1667

Online first article July 18, 2017 Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160684

Cylinders in del Pezzo surfaces with du Val singularities

Grigory Belousov

Plekhanov Russian University of Economics

Abstract

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Abstract

We consider del Pezzo surfaces with du Val singularities. We'll prove that a del Pezzo surface $X$ with du Val singularities has a $-K_X$-polar cylinder if and only if there exist tiger such that the support of this tiger does not contain anti-canonical divisor. Also we classify all del Pezzo surfaces $X$ such that $X$ has not any cylinders.

Keywords: cylinder, del Pezzo surface

MSC numbers: 14E07, 14E25, 14J45