We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ andprove some general result concerning the linear system $|H-P|$. We then look atregular surfaces lying on hypersurfaces of degree $s$ having a plane ofmultiplicity $(s-2)$. This implies that $S$ contains a plane curve. We provethat the degree of such surfaces is bounded and for $s=4$ we compute an actualbound.
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机译：我们考虑包含平面曲线$ P $的光滑表面$ S \ subset \ Pq $，并证明有关线性系统$ | H-P | $的一些一般结果。然后，我们查看位于度数为s $的超曲面上具有多重度为（s-2）的平面的规则曲面。这意味着$ S $包含一条平面曲线。我们证明了此类曲面的度是有界的，对于$ s = 4 $，我们计算了一个实际边界。
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