DEFORMATION CLASSES OF REAL FOUR-DIMENSIONAL CUBIC HYPERSURFACES


Creative Commons License

FİNASHİN S., Kharlamov V.

JOURNAL OF ALGEBRAIC GEOMETRY, vol.17, no.4, pp.677-707, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.1090/s1056-3911-08-00491-8
  • Journal Name: JOURNAL OF ALGEBRAIC GEOMETRY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.677-707

Abstract

We study real nonsingular cubic hypersurfaces X subset of 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,