论文标题
在理性表面上平稳的理性曲线
Smooth rational curves on rational surfaces
论文作者
论文摘要
考虑从固定射击曲线到投影表面的非恒定形态的方案。该方案与表面上有1美元的$ 1 $ CYCLE之间有一个合理的地图。我们证明，如果曲线是非敏感的，则该理性图是一种形态。结果，如果表面是有理的，并且我们修复了包含非单个理性曲线的除数类别，则该类别的方案参数化有理曲线是不可约的。此外，如果该类具有非负性自学，那么理性曲线方案就可以预期维度。
Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is non-singular, then this rational map is a morphism. As a consequence, we obtain that, if the surface is rational and we fix a divisor class containing a non-singular rational curve, then the scheme parametrizing rational curves on this class is irreducible. Further, if the class has non-negative self-intersection, then the scheme of rational curves has expected dimension.
