We show that the degree of smooth regular surfaces in P4 lying on a hypersurface of degree s containing a plane with multiplicity s-2 in its singular locus is bounded by a function of s. Then we show that a smooth regular surface lying on a quartic hypersurface with singular locus of dimension two has degree < 41.
On smooth surfaces in $\bold P\sp 4$ containing a plane curve
ELLIA, Filippo Alfredo;
2007
Abstract
We show that the degree of smooth regular surfaces in P4 lying on a hypersurface of degree s containing a plane with multiplicity s-2 in its singular locus is bounded by a function of s. Then we show that a smooth regular surface lying on a quartic hypersurface with singular locus of dimension two has degree < 41.File in questo prodotto:
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