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On smooth surfaces in P4 containing a plane curve

Ph. Ellia·C. Folegatti
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Abstract

We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of multiplicity $(s-2)$. This implies that $S$ contains a plane curve. We prove that the degree of such surfaces is bounded and for $s=4$ we compute an actual bound.

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Ph. Ellia, C. Folegatti. 2004-06-08. On smooth surfaces in P4 containing a plane curve. https://arxiv.org/abs/math/0310486

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