Deformation Classes of Real Four-dimensional Cubic Hypersurfaces
Algebraic Geometry
2008-04-30 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0607137,
title = {Deformation Classes of Real Four-dimensional Cubic Hypersurfaces},
author = {S. Finashin and V. Kharlamov},
journal= {arXiv preprint arXiv:math/0607137},
year = {2008}
}
Comments
25 pages, 3 figures