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math.AG1999
On codimension two subvarieties of P6
Philippe Ellia, Davide Franco
We prove the following: (a) Let X be a smooth, codimension two subvariety of P6. If X lies on a hyperquintic or if deg(X)<74, then X is a complete intersection. (b) Let X be a smoo…
math.AG1999
A note on rational surfaces in projective four-space
Philippe Ellia
It is proved that a smooth rational surface in projective four-space, which is ruled by cubics or quartics has degree at most 12. It is also proved that a smooth rational surface i…
math.AG1999
On smooth surfaces in projective four-space lying on quartic hypersurfaces with isolated singularities
Ph. Ellia, D. Franco
We prove that a smooth surface, non of general type, in projective four-space, which lies on a quartic hypersurface with isolated singularities has degree at most 27 (in fact we pr…