Viro's patchworking and the signed reduced A- discriminant

Computing the isotopy type of a hypersurface, defined as the positive real zero set of a polynomial, is a challenging problem in real algebraic geometry. For a fixed signed support, that is, for fixed exponent vectors and signs of the coefficients of the polynomial, the signed reduced -discriminant divides the coefficient space into chambers such that in each chamber the isotopy type of the hypersurfaces is constant. Within outer hambers the isotopy type of the hypersurface can be described by a olyhedral object. However, hypersurfaces associated with inner chambers might have isotopy types, which are more difficult to describe. In this talk, will discuss properties of the signed support that preclude the existence of such inner chambers of the signed reduced A-discriminant.