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International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh
October 22, 2013 12:15–13:15, Moscow, Steklov Mathematical Institute of RAS

On a combinatorial classification of minimal quasi-homogeneous 3-folds with a $SL(2)\times G_m$-action

V. V. Batyrev
 Video records: Flash Video 463.9 Mb Flash Video 2,779.4 Mb MP4 463.9 Mb

Abstract: The classification of minimal smooth projective quasi-homogeneous 3-folds with a $\mathrm{SL}(2)\times\mathbb{G}_m$-action has been known due to results of Mori, Mukai, Nakano, Moser-Jauslin, Kebekus, and Guan. The purpose of my talk is to explain a combinatorial approach to this classification using the Luna-Vust theory of spherical embeddings. This approach describes these minimal 3-folds by means of 2-dimensional fans of colored cones.