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Visible contours of real cubic surfaces

lundi 28-01-2013 à 15h30 (Salle de séminaires IRMA) - Séminaire Géométrie et applications

Sergey Finashin (METU, Ankara) : "Visible contours of real cubic surfaces"

Résumé : A visible contour of a cubic surface X in a projective 3-space is the curve formed by the critical values of the central projection mapping X to a plane. Such curve, C, is a sextic whose only singularities are six cusps lying on a conic, provided cubic X is non-singular and the center of projection is chosen outside X and generic. In a joint recent work with V.Kharlamov, we obtained an equisingular deformation classification of such visible contours C, in the real setting (i.e., over the ground field R). This is done by analysis of the lattice arithmetics of the real K3 surfaces, which are double covers of the plane ramified along C. An interesting unexpected outcome is splitting of these deformation classes (with a few exceptions) into pairs of partners, which looks like a kind of a ``strange`` duality.

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