Hilbert functions of chopped ideals

A chopped ideal is obtained from a homogeneous ideal by considering only the generators in a (low) degree. When the original ideal defines a sufficiently small number of points in projective space, chopping it does not alter the scheme. The complexity of computing these points from the chopped ideal is governed by the Hilbert function. We conjecture the values of this function and prove it in several cases. Using symbolic methods, we verify the conjecture for a large range of points. Our study of chopped ideals is motivated by symmetric tensor decomposition.