Geodesic
Toward Clemens' Conjecture in Degrees between 10 and 24
Serdica Mathematical Journal, Tome 23 (1997) no. 2, pp. 131-142.

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We introduce and study a likely condition that implies the following form of Clemens’ conjecture in degrees d between 10 and 24: given a general quintic threefold F in complex P^4, the Hilbert scheme of rational, smooth and irreducible curves C of degree d on F is finite, nonempty, and reduced; moreover, each C is embedded in F with balanced normal sheaf O(−1) ⊕ O(−1), and in P^4 with maximal rank.
Keywords: Rational Curves, Quintic Threefold 
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     title = {Toward {Clemens'} {Conjecture} in {Degrees} between 10 and 24},
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Johnsen, Trygve; Kleiman, Steven. Toward Clemens' Conjecture in Degrees between 10 and 24. Serdica Mathematical Journal, Tome 23 (1997) no. 2, pp. 131-142. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_2_a4/