On the geometric genus of subvarieties of generic hypersurfaces
Algebraic Geometry
2007-05-23 v1
Abstract
We prove some lower bounds on certain nonegative twists of the canonical bundle of a 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.
Keywords
Cite
@article{arxiv.math/0204256,
title = {On the geometric genus of subvarieties of generic hypersurfaces},
author = {Herbert Clemens and Ziv Ran},
journal= {arXiv preprint arXiv:math/0204256},
year = {2007}
}