Beyond a conjecture of Clemens
classification
🧮 math.AG
keywords
curvesgenericprovebeyondboundsbundlecanonicalcertain
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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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