Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Rational surfaces in index-one Fano hypersurfaces


Authors: Roya Beheshti and Jason Michael Starr
Journal: J. Algebraic Geom. 17 (2008), 255-274
DOI: https://doi.org/10.1090/S1056-3911-07-00459-6
Published electronically: December 5, 2007
MathSciNet review: 2369086
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Abstract | References | Additional Information

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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Additional Information

Roya Beheshti
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Address at time of publication: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
Email: beheshti@mast.queensu.ca; beheshti@math.wustl.edu

Jason Michael Starr
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: jstarr@math.mit.edu; jstarr@math.sunysb.edu

DOI: https://doi.org/10.1090/S1056-3911-07-00459-6
Received by editor(s): February 1, 2006
Received by editor(s) in revised form: April 10, 2006, and May 30, 2006
Published electronically: December 5, 2007
Additional Notes: The second author is supported by NSF grant DMS-0353692 and a Sloan Research Fellowship

American Mathematical Society