Let G be a flat finite-type group scheme over a scheme S, and X a noetherian S-scheme on which G-acts. We define and study G-prime and G-primary G-ideals on X and study their basic properties. In particular, we prove the existence of minimal G-primary decomposition and the well-definedness of G-associated G-primes. We also prove a generalization of Matijevic–Roberts type theorem. In particular,...

Given a plane graph G, we wish to nd a drawing of G in the plane such that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints without any edge-intersection. Such drawings are called planar straight-line drawings of G. An additional objective is to minimize the area of the rectangular grid in which G is drawn. In this...