Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Deformation classes of real four-dimensional cubic hypersurfaces


Authors: S. Finashin and V. Kharlamov
Journal: J. Algebraic Geom. 17 (2008), 677-707
DOI: https://doi.org/10.1090/S1056-3911-08-00491-8
Published electronically: March 3, 2008
MathSciNet review: 2424924
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Abstract | References | Additional Information

Abstract: We study real nonsingular cubic hypersurfaces $ X\subset P^5$ up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in $ H_4(X)$. Moreover, we provide a graph $ \Gamma_{K4}$ whose vertices represent the equivalence classes of such cubics and whose edges represent their adjacency. It turns out that the graph $ \Gamma_{K4}$ essentially coincides with the graph $ \Gamma_{K3}$ characterizing a certain adjacency of real nonpolarized K3-surfaces.


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Additional Information

S. Finashin
Affiliation: Middle East Technical University, Department of Mathematics, Ankara 06531 Turkey
Email: serge@metu.edu.tr

V. Kharlamov
Affiliation: Louis Pasteur et IRMA (CNRS)\endgraf7 rue René Descartes 67084 Strasbourg Cedex, France
Email: kharlam@math.u-strasbg.fr

DOI: https://doi.org/10.1090/S1056-3911-08-00491-8
Received by editor(s): July 5, 2006
Received by editor(s) in revised form: May 2, 2007
Published electronically: March 3, 2008
Additional Notes: The second author is supported by ANR-05-BLAN-0053-01.

American Mathematical Society