Complexes which arise from a matrix and a vector: Resolutions of divisors on certain varieties of complexes (Q1310414)

Let \(R_ 0\) be a normal domain and \(R = R_ 0 [X,Y]\), where \(X\) and \(Y\) are matrices of indeterminates \(1 \times g\), resp. \(g \times f)\). The \(R\)-ideal \(J = I_ 1 (XY) + I_{\min (f,g)} (Y)\) defines a variety of complexes over \(R_ 0\). The divisor class group Cl\( (R/J)\) is isomorphic to Cl\( (R_ 0) \oplus \mathbb{Z} [I']\), where \(I'\) is an ideal of \(R/J\) generated by suitably choosen lower order minors of \(Y\). The minimal \(R\)- free resolution of \(i[I']\) for all integers \(i \geq -1\) is produced. This long and technical paper is related to previous research [the author and \textit{B. Ulrich}, Mem. Am. Math. Soc. 461 (1992; Zbl 0753.13005)].