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arXiv · alg-geom/9601024

Toward Clemens' Conjecture in degrees between 10 and 24

Trygve Johnsen·Steven L. Kleiman
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Abstract

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 $\IP^4$, 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 $Ø(-1)\oplusØ(-1)$, and in $\IP^4$ with maximal rank.

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BibTeXRIS

Trygve Johnsen, Steven L. Kleiman. 1996-03-22. Toward Clemens' Conjecture in degrees between 10 and 24. https://arxiv.org/abs/alg-geom/9601024

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