The associated-form conjecture for invariants of degree-\n(m-2) forms
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.
Sources & referencesView supporting material
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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