Rational surfaces in index-one fano hypersurfaces

Beheshti Roya; Michael Starr Jason

doi:10.1090/s1056-3911-07-00459-6

Rational surfaces in index-one fano hypersurfaces

Beheshti Roya
, Michael Starr Jason

Mathematics

Queen's University Kingston
Washington University St. Louis

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

8 Scopus citations

Abstract

We give the first evidence for a conjecture that a general, index-one, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by low-degree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.

Original language	English
Pages (from-to)	255-274
Number of pages	20
Journal	Journal of Algebraic Geometry
Volume	17
Issue number	2
DOIs	https://doi.org/10.1090/s1056-3911-07-00459-6
State	Published - 2008

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abstract = "We give the first evidence for a conjecture that a general, index-one, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by low-degree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.",

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AB - We give the first evidence for a conjecture that a general, index-one, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by low-degree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.

UR - https://www.scopus.com/pages/publications/77952195429

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JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

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Rational surfaces in index-one fano hypersurfaces

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