Deformation Classes of Real Four-dimensional Cubic Hypersurfaces

Details Deformation Classes of Real Four-dimensional Cubic Hypersurfaces Deformation Classes of Real Four-dimensional Cubic Hypersurfaces

2006-07-05

arxiv.org/abs/math/0607137v1

Mathematics

Algebraic Geometry

25 pages, 3 figures

Scientific paper

We study real nonsingular projective cubic fourfolds 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 the middle homology. Moreover, we provide a graph whose vertices represent the equivalence classes of such cubics and edges represent their adjacency. It turns out that this graph essentially coincides with the graph characterizing a certain adjacency of real non-polarized K3-surfaces.

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