## The Michigan Mathematical Journal

### Smooth Rational Curves on Singular Rational Surfaces

Ziquan Zhuang

#### Abstract

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 $p\in X$, there is a smooth curve (locally analytically) passing through $p$, then $X$ contains at least one smooth rational curve.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1508810820

Digital Object Identifier
doi:10.1307/mmj/1508810820

Mathematical Reviews number (MathSciNet)
MR3770854

Zentralblatt MATH identifier
06965590

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

#### Citation

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

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