The module of logarithmic derivations of a generic determinantal ideal.

An important problem in algebra and related fields (such as algebraic and complex analytic geometry) is to find an explicit, well-structured, minimal set of generators for the module of logarithmic derivations of classes of homogeneous ideals in polynomial rings. In this note we settle the case of the ideal P ⊂ R = K[{X_i,j}] generated by the maximal minors of an (n + 1) × n generic matrix (X_i,j) over an arbitrary field K with n ≥ 2. We also characterize when the derivation module of R/P is Ulrich, and we investigate this property if we replace R/P by determinantal rings arising from simple degenerations of the generic case. [ABSTRACT FROM AUTHOR]