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Rational curves of degree 10 on a general quintic threefold

Ethan Cotterill
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Abstract

We prove the "strong form" of the Clemens conjecture in degree 10. Namely, on a general quintic threefold F in P^4, there are only finitely many smooth rational curves of degree 10, and each curve is embedded in F with normal bundle O(-1)^2. Moreover, in degree 10, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with rational components in F.

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Ethan Cotterill. 2004-12-16. Rational curves of degree 10 on a general quintic threefold. https://arxiv.org/abs/math/0412002

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