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Viro method for the construction of real complete intersections. (English) Zbl 1048.14035
Summary: The Viro method is a powerful construction method of real nonsingular algebraic hypersurfaces with prescribed topology [O. Viro, in: Topology conference, Proc., Collect. Rep., Leningrad 1982, 149–197 (1983; Zbl 0605.14021)]. It is based on polyhedral subdivisions of Newton polytopes. A combinatorial version of the Viro method is called combinatorial patchworking and arises when the considered subdivisions are triangulations. B. Sturmfels [Ann. Sc. Norm. Super. Pisa (4) 21, 377–386 (1994; Zbl 0826.14032)] generalized the combinatorial patchworking to the case of real complete intersections. The author extends this result by generalizing the Viro method to the case of real complete intersections.
14P25Topology of real algebraic varieties
14M10Complete intersections
14M25Toric varieties, Newton polyhedra