An improved bound for the degree of smooth surfaces in P4 not of general type.

Details An improved bound for the degree of smooth surfaces in P4 not of general type. An improved bound for the degree of smooth surfaces in P4 not of general type.

1995-01-16

arxiv.org/abs/alg-geom/9501005v1

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.

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