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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.
MSC:
14P25Topology of real algebraic varieties
14M10Complete intersections
14M25Toric varieties, Newton polyhedra