The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 67, Issue 1 (2018), 83-98.
Smooth Rational Curves on Singular Rational Surfaces
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 is a log del Pezzo surface such that, for every closed point , there is a smooth curve (locally analytically) passing through , then contains at least one smooth rational curve.
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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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