turkmath.org

There is an interesting map which assigns to a homogeneous form $f$ on $\mathbb{C}$ of degree $d$ with non-vanishing discriminant, a certain form on $\mathbb{C}$ of degree $n(d − 2)$. It was conjectured in a recent paper by M. Eastwood and A. Isaev that all absolute classical invariants of forms on $\mathbb{C}$ of degree $d$ can be extracted from those of forms of degree $n(d − 2)$ via this map. This surprising conjecture was motivated by the well-known Mather-Yau theorem for isolated hypersurface singularities. I will report on joint work with A.Isaev which settles this conjecture in full generality and proves a stronger statement in the case of binary forms.