Ideals associated to two sequences and a matrix

Abstract

Abstract. Let u 1×n , X n×n , and v n×1 be matrices of indeterminates, Adj X be the classical adjoint of X, and H(n) be the ideal I 1 (uX) + I 1 (Xv) + I 1 (vu − Adj X). Vasconcelos has conjectured that H(n) is a perfect Gorenstein ideal of grade 2n. In this paper, we obtain the minimal free resolution of H(n); and thereby establish Vasconcelos' conjecture.Let u 1×n , X n×n , and v n×1 be matrices of indeterminates over a commutative noetherian ring R 0 , and let H(n) be the ideal I 1 (uX) + I 1 (Xv) + I 1 (vu − Adj X) of the polynomial ring R = R 0 [{u i , v i