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On the geometric genus of subvarieties of generic hypersurfaces

Herbert Clemens·Ziv Ran
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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.

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Herbert Clemens, Ziv Ran. 2002-04-20. On the geometric genus of subvarieties of generic hypersurfaces. https://arxiv.org/abs/math/0204256

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