Rational curves on smooth cubic hypersurfaces

Izzet Coskun; Jason Starr

doi:10.1093/imrn/rnp102

Rational curves on smooth cubic hypersurfaces

Izzet Coskun
, Jason Starr

Mathematics

University of Illinois at Chicago

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

37 Scopus citations

Abstract

We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hyper-surface in ℙⁿ of degree 2d ≤ min (n + 4, 2n - 2) and dimension at least three is irreducible and of the expected dimension.

Original language	English
Pages (from-to)	4626-4641
Number of pages	16
Journal	International Mathematics Research Notices
Issue number	24
DOIs	https://doi.org/10.1093/imrn/rnp102
State	Published - 2009

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10.1093/imrn/rnp102

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title = "Rational curves on smooth cubic hypersurfaces",

abstract = "We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hyper-surface in ℙn of degree 2d ≤ min (n + 4, 2n - 2) and dimension at least three is irreducible and of the expected dimension.",

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AU - Starr, Jason

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N2 - We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hyper-surface in ℙn of degree 2d ≤ min (n + 4, 2n - 2) and dimension at least three is irreducible and of the expected dimension.

AB - We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hyper-surface in ℙn of degree 2d ≤ min (n + 4, 2n - 2) and dimension at least three is irreducible and of the expected dimension.

UR - https://www.scopus.com/pages/publications/77955902027

U2 - 10.1093/imrn/rnp102

DO - 10.1093/imrn/rnp102

M3 - Article

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SN - 1073-7928

SP - 4626

EP - 4641

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 24

ER -

Rational curves on smooth cubic hypersurfaces

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