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 P n / G , where G is a subgroup of the symmetric group Σ n + 1 acting on P n by permuting the projective coordinates. For bilinear forms, we give a similar stratification up to dimension 4. [ABSTRACT FROM AUTHOR]