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Beyond a conjecture of Clemens

Ziv Ran
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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.

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Ziv Ran. 2000-05-03. Beyond a conjecture of Clemens. https://arxiv.org/abs/math/9911161

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