Curves of small degree on cubic threefolds

Joe Harris; Mike Roth; Jason Starr

doi:10.1216/rmjm/1181069707

Curves of small degree on cubic threefolds

Joe Harris
, Mike Roth
, Jason Starr

Mathematics

Harvard University
University of Michigan, Ann Arbor

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

In this article we consider the spaces H^{d, g}(X) parametrizing smooth curves of degree d and genus g on a smooth cubic threefold X ⊂ P⁴. For 1 ≤ d ≤ 5, we show that each variety H^{d, g}(X) is irreducible of dimension 2d.

Original language	English
Pages (from-to)	761-817
Number of pages	57
Journal	Rocky Mountain Journal of Mathematics
Volume	35
Issue number	3
DOIs	https://doi.org/10.1216/rmjm/1181069707
State	Published - 2005

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title = "Curves of small degree on cubic threefolds",

abstract = "In this article we consider the spaces Hd, g(X) parametrizing smooth curves of degree d and genus g on a smooth cubic threefold X ⊂ P4. For 1 ≤ d ≤ 5, we show that each variety Hd, g(X) is irreducible of dimension 2d.",

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AB - In this article we consider the spaces Hd, g(X) parametrizing smooth curves of degree d and genus g on a smooth cubic threefold X ⊂ P4. For 1 ≤ d ≤ 5, we show that each variety Hd, g(X) is irreducible of dimension 2d.

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DO - 10.1216/rmjm/1181069707

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JO - Rocky Mountain Journal of Mathematics

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Curves of small degree on cubic threefolds

Abstract

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