Appears in collection : 2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

A classical method to compute with sparse polynomials is to homogenize them with respect to Newton polytopes, regarding them as homogeneous elements of Cartier degrees in the Cox ring of a projective toric variety. In this talk, we investigate subvarieties defined by generic polynomial systems in the Cox ring when the degrees are non-necessarily Cartier, with a view towards identifying alternative toric homogenizations that are suitable for practical computations. Joint work with Matías Bender.