On smooth surfaces in P4 containing a plane curve

Details On smooth surfaces in P4 containing a plane curve On smooth surfaces in P4 containing a plane curve

2003-10-31

arxiv.org/abs/math/0310486v3

Mathematics

Algebraic Geometry

10 pages. The content has been replaced since there was an error in the proof of the main theorem

Scientific paper

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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