Ziv Ran
Published 1999-11-21, updated 2000-05-03Version 2
We prove some lower bounds on certain twists of the canonical bundle of a codimension-2 subvariety of a generic hypersurface in projective space. In particular we prove that the generic sextic threefold contains no rational or elliptic curves and no nondegenerate curves of genus 2.
Comments: Statements and proofs have been modified. In some cases the results are now stronger. In particular, we prove that a generic sextic 3-fold contains no rational or elliptic curves, and no nondegenerate curves of genus 2, which goes beyond Clemens' original conjecture
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