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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
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
MR Author ID: 244559

V. Kharlamov
Affiliation: Louis Pasteur et IRMA (CNRS)\endgraf7 rue René Descartes 67084 Strasbourg Cedex, France
MR Author ID: 202474
ORCID: 0000-0001-9341-1391

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.