Beyond a conjecture of Clemens
Algebraic Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/9911161,
title = {Beyond a conjecture of Clemens},
author = {Ziv Ran},
journal= {arXiv preprint arXiv:math/9911161},
year = {2007}
}
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