Rational curves of degree 10 on a general quintic threefold
Abstract
Description
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.
The justification of Fact 1 on p. 10 has been made clearer; minor formatting issues and typos corrected. To appear in Communications in Algebra
The justification of Fact 1 on p. 10 has been made clearer; minor formatting issues and typos corrected. To appear in Communications in Algebra