On smooth surfaces in $\bold P\sp 4$ containing a plane curve
Ellia, Ph. ; Folegatti, C.
Illinois J. Math., Tome 51 (2007) no. 3, p. 339-352 / Harvested from Project Euclid
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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 $\deg(S) \leq 40$.
Publié le : 2007-04-15
Classification:  14J25 
@article{1258138417,
     author = {Ellia, Ph. and Folegatti, C.},
     title = {On smooth surfaces in $\bold P\sp 4$ containing a plane curve},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 339-352},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138417}
}

Ellia, Ph.; Folegatti, C. On smooth surfaces in $\bold P\sp 4$ containing a plane curve. Illinois J. Math., Tome 51 (2007) no. 3, pp.  339-352. http://gdmltest.u-ga.fr/item/1258138417/