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Summer 2004 Cubic fourfolds and spaces of rational curves
Jason Starr, A. J. de Jong
Illinois J. Math. 48(2): 415-450 (Summer 2004). DOI: 10.1215/ijm/1258138390

Abstract

For a general nonsingular cubic fourfold $X\subset \PP^5$ and $e\geq 5$ an odd integer, we show that the space $M_e$ parametrizing rational curves of degree $e$ on $X$ is non-uniruled. For $e \geq 6$ an even integer, we prove that the generic fiber dimension of the maximally rationally connected fibration of $M_e$ is at most one, i.e., passing through a very general point of $M_e$ there is at most one rational curve. For $e < 5$ the spaces $M_e$ are fairly well understood and we review what is known.

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Jason Starr. A. J. de Jong. "Cubic fourfolds and spaces of rational curves." Illinois J. Math. 48 (2) 415 - 450, Summer 2004. https://doi.org/10.1215/ijm/1258138390

Information

Published: Summer 2004
First available in Project Euclid: 13 November 2009

zbMATH: 1081.14007
MathSciNet: MR2085418
Digital Object Identifier: 10.1215/ijm/1258138390

Subjects:
Primary: 14C05
Secondary: 14E08

Rights: Copyright © 2004 University of Illinois at Urbana-Champaign

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Vol.48 • No. 2 • Summer 2004
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