Rational curves of degree at most 9 on a general quintic threefold

@inproceedings{Johnsen1996RationalCO,
  title={Rational curves of degree at most 9 on a general quintic threefold},
  author={T. Johnsen and Steven L. KLEIMAN},
  year={1996}
}
We prove the following form of the Clemens conjecture in low degree. Let d ≤ 9, and let F be a general quintic threefold in P. Then (1) the Hilbert scheme of rational, smooth and irreducible curves of degree d on F is finite, nonempty, and reduced; moreover, each curve is embedded in F with normal bundle O(−1) ⊕O(−1), and in P with maximal rank. (2) On F… CONTINUE READING