Stability of associated forms

Abstract

We show that the associated form, or equivalently a Macaulay inverse system, of an Artinian complete intersection of type $(d,\dots ,d)$ is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities.

20 pages, to appear in Journal of Algebraic Geometry. v5: agrees with accepted version, except for formatting