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arXiv · 1604.02166

Smooth Rational Curves on Singular Rational Surfaces

Ziquan Zhuang
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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.

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Ziquan Zhuang. 2016-04-07. Smooth Rational Curves on Singular Rational Surfaces. https://doi.org/10.1307/mmj/1508810820

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