论文标题
在光滑的Hermitian表面II上的理性曲线II
Rational curves on a smooth Hermitian surface II
论文作者
论文摘要
在特征性$ p> 0 $中，对于$ p $ $ p $的$ q $，我们计算了在光滑的Hermitian $ q+1 $上的非平面理性曲线的数量，假设曲线具有多项式的参数化，最多可$ 4 $。结果表明，光滑的Hermitian立方体表面包含无限的许多理性曲线$ 3 $和$ 6 $。另一方面，在所有其他情况下，曲线的数量是有限的，并且是精确确定的。进一步的这样的理性曲线被明确地达到了投影性同构，并检查了它们的平滑度。
In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by polynomials with at most $4$ terms. It is shown that a smooth Hermitian cubic surface contains infinitely many rational curves of degree $3$ and $6$. On the other hand, for all other cases the numbers of curves are finite and they are exactly determined. Further such rational curves are given explicitly up to projective isomorphism and their smoothness are checked.
