Beyond a conjecture of Clemens
Abstract
Description
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.
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
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