Stratification of moduli spaces of Lie algebras, similar matrices and bilinear forms

In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of n×n matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give a complete description of a stratification of the space by some very simple projective orbifolds of the form Pn/G, where G is a subgroup of the symmetric group Σn+1 acting on Pn by permuting the projective coordinates. For bilinear forms, we give a similar stratification up to dimension 4.