Algebraic properties of grids of projective lines (Q861854)

A complete grid is the projective closure of affine lines which are parallel to the coordinate axes and pass through a lattice of points. In the paper under review, the authors compute the generators and, in case of \(\mathbb{P}^3\), the Hilbert function of complete grids. They also study the Cohen-Macaulay and seminormality properties of the homogeneous coordinate ring of a (complete and, in the case of \(\mathbb{P}^3\), also incomplete) grid.