Abstract
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 C is embedded in F with normal bundle 𝒪(−1) ⊕ 𝒪(−1). Moreover, in degree 10, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with rational components on F.
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