A matrix of linear forms which is annihilated by a vector of indeterminates

Let R = k[T-1, . . . ,T-f] be a standard graded polynomial ring over the field kappa and Psi be an f x g matrix of linear forms from R, where 1 <= g < f. Assume [T-1 . . . T-f] If is 0 and that grade I-g(Psi) is exactly one short of the maximum possible grade. We resolve (R) over bar = R/I-g(Psi), prove that (R) over bar has a g-linear resolution, record explicit formulas for the h-vector and multiplicity of (R) over bar, and prove that if f - g is even, then the ideal I-g (Psi) is unmixed. Furthermore, if f - g is odd, then we identify an explicit generating set for the unmixed part, I-g (Psi)(uam), of I-g(Psi), resolve R/I-g(Psi)(unm), and record explicit formulas for the h-vector of R/I-g(Psi)(unm).(The rings R/I-g(Psi) and R/I-g (Psi)(unm) automatically have the same multiplicity.) These results have applications to the study of the blow-up algebras associated to linearly presented grade three Gorenstein ideals. (C) 2016 Elsevier Inc. All rights reserved.