Rational curves on a general heptic fourfold
type: Item
instance of: scholarly article
title: Rational curves on a general heptic fourfold
zbMATH Open document ID: 1183.14059
author: Trygve Johnsen
author: Gert Monstad Hana
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2010-01-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1260369404
review text: The authors study rational curves on a general hypersurface \(X\) of degree \(7\), in the complex projective 5-space. It is known that \(X\) contains a finite number of lines, and the authors conjecture that these lines are the only rational curves on \(X\). The authors are able to prove that, for \(d\) between \(2\) and \(15\), there is no rational curve of degree \(d\) on \(X\). The result is proved by studying the generic initial ideal of a general hyperplane section of a rational curve. The procedure was introduced by Cotterill, for the study of rational curves on a general quintic threefold in the 4-space.
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14J35
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 5658088
zbMATH Keywords: fourfolds
zbMATH Keywords: rational curves
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5658088