Parsa Saberi

An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds

We prove a necessary condition conjecture ([27, Conjecture B]) for the maximal singularity of the Hilbert scheme of points in 3D for a large class of degrees, which in particular implies the 1978 Brian\c{c}on-Iarrobino Conjecture for a tetrahedral degree, and vastly generalises the result in [19]. The novelty lies in i...