Toward Clemens' Conjecture in degrees between 10 and 24

Trygve Johnsen; Steven L. Kleiman

Toward Clemens' Conjecture in degrees between 10 and 24

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: Trygve Johnsen , Steven L. Kleiman

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

Keywords

algebraic curves hilbert scheme conjectures and proofs

Cite

@article{arxiv.alg-geom/9601024,
  title  = {Toward Clemens' Conjecture in degrees between 10 and 24},
  author = {Trygve Johnsen and Steven L. Kleiman},
  journal= {arXiv preprint arXiv:alg-geom/9601024},
  year   = {2008}
}

Comments

Plain Tex, This eleven page paper is a joint manuscript, produced in connection with the first author's participation in the conference "Geometry and Physics", Zlatograd, Bulgaria, August 28 - Sept.2, 1995." This version contains a small change in Remark (3.3); the hope expressed there has been refined

Toward Clemens' Conjecture in degrees between 10 and 24

Abstract

Keywords

Cite

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