Associated Forms in Classical Invariant Theory and Their Applications to Hypersurface Singularities

Abstract

It was conjectured in the recent article [EI] that all absolute classical invariants of forms of degree m ≥ 3 on C can be extracted, in a canonical way, from those of forms of degree n(m−2) by means of assigning every form with non-vanishing discriminant the so-called associated form. This surprising conjecture was confirmed in [EI] for binary forms of degree m ≤ 6 and ternary cubics. In the present paper, we settle the conjecture in full generality. In addition, we propose a stronger version of this statement and obtain evidence supporting it.

Cite this paper

@inproceedings{Alper2014AssociatedFI, title={Associated Forms in Classical Invariant Theory and Their Applications to Hypersurface Singularities}, author={Jarod Alper and Alexander Isaev}, year={2014} }