A Combinatorial Proof of the Smoothness of Catalecticant Schemes Associated to Complete Intersections

For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant schemes along an open subset of a particular irreducible component.We acknowledge the support of the Australian Research Council by way of Discovery Project DP140100296