RATIONAL CURVES OF DEGREE 11 ON A GENERAL QUINTIC 3-FOLD

We prove that the incidence scheme of rational curves of degree 11 in quintic 3-folds is irreducible. Irreducibility implies a strong form of the Clemens conjecture in degree 11; namely, on a general quintic 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 풪(−1) ⊕ 풪(−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.