논문KCI 등재
Cylinders in del Pezzo surfaces with du Val singularities
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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.
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.
참고문헌 (7)
- I. Cheltsov, "Cylinders in singular del Pezzo surfaces", Compos. Math, 152(6), pp.1198~1224 (2016)
- I. Cheltsov, "Affne cones over smooth cubic surfaces", J. Eur. Math. Soc, 18(7), pp.1537~1564 (2016)
- R. Hartshorne, "Algebraic Geometry" (1977), Springer Science+Business Media, Inc.
- S. Keel, "Rational curves on quasi-projective surfaces", Mem. Amer. Math. Soc, 140(669), pp.153~ (1999)
- T. Kishimoto, "Group actions on affine cones, Affine algebraic geometry, CRM Proc. Lecture Notes, 54", Amer. Math. Soc., 123~163 (2011)
- T. Kishimoto, "Ga-actions on affine cones", Transform. Groups, 18(4), pp.1137~1153 (2013)
- K. Matsuki, "Introduction to the Mori Program" (2002), Springer-Verlag New York, Inc.
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