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Curves Contained in a Hyperplane Section of a General Quintic 3-fold
by Edoardo Ballico

Vol. 11 No. 2 (2016) P.393~P.399

ABSTRACT

Let $W\subset \mathbb{P}^4$ a very general quintic hypersurface. We study the existence/non-existence of non-complete intersection curves $T\subset W$ with $T$ spanning a hyperplane $H$ and $H\cap W$ smooth (non-existence if the hyperplanes vary in a family not containing a line or a conic of $W$).

KEYWORDS
Quintic 3-fold; complete intersection; Clemens' conjecture; space curves; Noether-Lefschetz; space curve.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 14M10; 14C22; 14M05.

MILESTONES