Rational curves of degree 11 on a general quintic threefold

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We prove that the incidence scheme of rational curves of degree 11 on quintic threefolds is irreducible. This implies a strong form of the Clemens conjecture in degree 11. Namely, on a general quintic threefold F in P⁴, there are only finitely many smooth rational curves of degree 11, and each curve C is embedded in F with normal bundle O(-1) ⊕ O(-1). Moreover, in degree 11, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with rational components on F.