Mathematics – Algebraic Geometry
Scientific paper
1995-01-16
Mathematics
Algebraic Geometry
5 pages, Latex version 2.09, no figures.
Scientific paper
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.
Cook Michele
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