Cubic fourfolds and spaces of rational curves
type: Item
instance of: scholarly article
title: Cubic fourfolds and spaces of rational curves
zbMATH Open document ID: 1081.14007
published in: Illinois Journal of Mathematics
publication date: 2005-02-25T00:00:00Z
review text: Let \(X\) be a nonsingular cubic fourfold \(X\subset\mathbb{P}^5\) and denote by \(M_e\) the scheme of rational curves of degree \(e\) in \(X\). The authors prove that, for \(X\) general and \(e\geq 5\) an odd integer, the space \(M_e\) is non-uniruled. Moreover for \(e\geq 6\) an even integer, they prove that the generic fiber dimension of the maximally rationally connected fibration of \(M_e\) is at most one. The authors use different compactifications of \(M_e\) by means of Hilbert schemes, Chow varieties and Kontsevich moduli spaces of stable maps. They prove also that the scheme \(M_e\) is an irreducible variety of dimension \(3e+ 1\).
reviewed by: Luciana Ramella
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 2138865
zbMATH Keywords: moduli spaces
zbMATH Keywords: Deligne-Mumford stacks
zbMATH Keywords: rationally connected varieties
author: Aise Johan de Jong
author: Jason Michael Starr
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2138865