## Illinois Journal of Mathematics

### On smooth surfaces in $\bold P\sp 4$ containing a plane curve

#### Abstract

Let $\Sigma \subset \mathbb{P}^4$ be an integral hypersurface of degree $s$ with a $(s-2)$-uple plane. We show that the degrees of smooth surfaces $S \subset \Sigma$ with $q(S)=0$ are bounded by a function of $s$. We also show that if $S \subset \mathbb{P}^4$ is a smooth surface with $q(S)=0$ and if $S$ lies on a quartic hypersurface $\Sigma$ such that $\dim(\Sing(\Sigma))=2$, then $\deg(S) \leq 40$.

#### Article information

Source
Illinois J. Math., Volume 51, Number 2 (2007), 339-352.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138417

Digital Object Identifier
doi:10.1215/ijm/1258138417

Mathematical Reviews number (MathSciNet)
MR2342662

Zentralblatt MATH identifier
1126.14055

#### Citation

Ellia, Ph.; Folegatti, C. On smooth surfaces in $\bold P\sp 4$ containing a plane curve. Illinois J. Math. 51 (2007), no. 2, 339--352. doi:10.1215/ijm/1258138417. https://projecteuclid.org/euclid.ijm/1258138417