Let be any field. Given linear forms in , some possibly proportional, in one of our main results we show that the ideal generated by all -fold products of these linear forms has linear graded free resolution. When no two of the linear forms considered are proportional, this result helps determining a complete set of generators of the symmetric ideal of . Via Sylvester forms we can analyze from a different perspective the generators of the presentation ideal of the Orlik–Terao algebra of the second order; this is the algebra generated by the reciprocals of the products of any two (distinct) of the linear forms considered.
"On ideals generated by -fold products of linear forms." J. Commut. Algebra 13 (4) 549 - 570, Winter 2021. https://doi.org/10.1216/jca.2021.13.549