Radical support for multigraded ideals

Abstract Can one tell if an ideal is radical just by looking at the degrees of generators? In general, this hopeless. However, there are special collections in multigraded polynomial rings, with property that any generated elements those radical. We call such a collection support. paper, we give combinatorial characterization supports. Our terms properties cycles associated labelled graph. also show notion support closely related to Cartwright-Sturmfels ideals. fact, generators whose multidegrees form ideal. Conversely,