Toward Clemens' Conjecture in degrees between 10 and 24

1996/01/23 by Trygve Johnsen, Steven L. Kleiman, Johnsen, Trygve +1 · 1 citation
Arts and Humanities · #American Literature and Humor Studies

paper · pdf · doi:10.48550/arxiv.alg-geom/9601024

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 \IP⁴, 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)⊕Ø(-1), and in \IP⁴ with maximal rank.

Cited by

• Rational curves of degree 10 on a general quintic threefold

Related

• Rational curves of degree at most 9 on a general quintic threefold
• Rational curves of degree 10 on a general quintic threefold
• Rational curves of degree 10 on a general quintic threefold
• Clemens' conjecture: part I
• Finiteness of rational curves of degree 12 on a general quintic threefold