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Smooth Rational Curves on Singular Rational Surfaces. (arXiv:1604.02166v2 [math.AG] UPDATED)

来源于:arXiv
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. 查看全文>>