2013/08/29 by Jarod Alper, Alper, Jarod, Alexander Isaev +1
Mathematics · #13A50 #13H10 #14L24 #32S25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #math.AC #math.AG #math.CV #msc:13A50 #msc:13H10 #msc:14L24 #msc:32S25
paper · pdf · doi:10.48550/arxiv.1308.6624
arxiv created 2013/08/29 · arxiv updated 2013/09/02
It was conjectured in a recent article by M. Eastwood and the second author that all absolute classical invariants of forms of degree m≥ 3 on \mathbb Cn 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. In that paper, this surprising conjecture was confirmed for binary forms of degree m ≤ 6 and ternary cubics. In the present article, we settle the conjecture in full generality. In addition, we propose a stronger version of this statement and obtain evidence supporting it.