DEFORMATION CLASSES OF REAL FOUR-DIMENSIONAL CUBIC HYPERSURFACES


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FİNASHİN S. , Kharlamov V.

JOURNAL OF ALGEBRAIC GEOMETRY, cilt.17, sa.4, ss.677-707, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 17 Konu: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1090/s1056-3911-08-00491-8
  • Dergi Adı: JOURNAL OF ALGEBRAIC GEOMETRY
  • Sayfa Sayıları: ss.677-707

Özet

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,