Smooth rationally connected threefolds contain all smooth curves

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Sankaran, G. K.
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Abstract
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We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We give some details about the toric case.
Comment: Version 1 was called "Any smooth toric threefold contains all curves". This version is completely rewritten and proves a much stronger result, following suggestions of Janos Kollar
Keywords
Mathematics - Algebraic Geometry, 14E25, 14H99, 14M22, 14M25
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