Smooth surfaces S in P^4 containing a 1-dimensional family of plane curves not forming a fibration are studied. We obtain some results confirming the conjecture that the Veronese surface and the quintic elliptic scrolls are the only ones that do not lie on a quadric cone.
Some remarks on surfaces in P^4 containing a family of plane curves / J.C. Sierra, A.L. Tironi. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 209:2(2007 May), pp. 361-369.
Some remarks on surfaces in P^4 containing a family of plane curves
A.L. TironiUltimo
2007
Abstract
Smooth surfaces S in P^4 containing a 1-dimensional family of plane curves not forming a fibration are studied. We obtain some results confirming the conjecture that the Veronese surface and the quintic elliptic scrolls are the only ones that do not lie on a quadric cone.
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