Viro Method for the Construction of Real Complete Intersections

AbstractThe Viro method is a powerful construction method of real nonsingular algebraic hypersurfaces with prescribed topology. 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 has generalized the combinatorial patchworking to the case of real complete intersections. We extend his result by generalizing the Viro method to the case of real complete intersections