Clemens' conjecture for octic and nonic curves
type: Item
instance of: scholarly article
title: Clemens' conjecture for octic and nonic curves
zbMATH Open document ID: 0910.14012
DOI: 10.1016/0019-3577(95)91244-P
author: Pieter G. J. Nijsse
published in: Indagationes Mathematicae. New Series
publication date: 1999-04-20T00:00:00Z
review text: Clemens conjectured that on a general quintic threefold \(F\) in \(\mathbb{P}^4\) there are only finitely many smooth rational curves of a given degree \(d\) [\textit{H. Clemens} in: Topics in transcendental algebraic geometry, Ann. Math. Stud. 106, 289-304 (1984; Zbl 0575.14007), p. 300]. \textit{S. Katz} published a proof for \(d\leq 7\) [Compos. Math. 60, 151-162 (1986; Zbl 0606.14039); \S 1.2]. Here we will consider the degrees \(d=8\) and 9. Main theorem. The space of smooth rational curves of degree \(\leq 9\) on a general quintic in \(\mathbb{P}^4\) is finite, nonempty and reduced.
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 792826
zbMATH Keywords: octic curves
zbMATH Keywords: nonic curves
zbMATH Keywords: curves on a general quintic
Wikidata QID: Q123015177
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 792826