The Michigan Mathematical Journal

Smooth Rational Curves on Singular Rational Surfaces

Ziquan Zhuang

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We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary, we show that if X is a log del Pezzo surface such that, for every closed point pX, there is a smooth curve (locally analytically) passing through p, then X contains at least one smooth rational curve.

Article information

Michigan Math. J., Volume 67, Issue 1 (2018), 83-98.

Received: 8 August 2016
Revised: 25 January 2017
First available in Project Euclid: 24 October 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M22: Rationally connected varieties
Secondary: 14J26: Rational and ruled surfaces


Zhuang, Ziquan. Smooth Rational Curves on Singular Rational Surfaces. Michigan Math. J. 67 (2018), no. 1, 83--98. doi:10.1307/mmj/1508810820.

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