%0 Journal Article
%T An improved bound for the degree of smooth surfaces in P4 not of general type.
%A Michele Cook
%J Mathematics
%D 1995
%I arXiv
%X This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound for the degree of a smooth surface in $\pfour$ not of general type. Using their construction and the regularity of curves in $\pthree$, one may lower the bound a little more. We will prove the following: Theorem. Let $S$ be a smooth surface of degree $d$ in $\pfour$ not of general type. Then either $d \leq 70$ or $S$ lies on a hypersurface in $\pfour$ of degree 5 and $d \leq 80$. Thus $d \leq 80$. We will also indicate how to lower the bound to 76.
%U http://arxiv.org/abs/alg-geom/9501005v1