The associated-form conjecture for invariants of degree-\n(m-2) forms
Let be the space of degree- forms in variables, and let denote the relevant algebra of invariants of such forms. For , let be a form associated to , meaning a highest-degree form of degree on arising from the nil-polynomial of the associated Artinian Gorenstein algebra.
Associated-form conjecture. For any there exists an absolute invariant of forms of degree on such that, for all , the invariant is defined at some (hence at every) form associated to and
The conjecture proposes that every invariant of degree- forms can be recovered from an absolute invariant of their associated forms. It was essentially verified for binary quartics (, ) and ternary cubics (, ), but the general statement is resolved according to the supplied status evidence.
References
Primary source
M. G. Eastwood and A. V. Isaev, “Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities”, arXiv:1402.6049 (2014).
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