The module of logarithmic derivations of a generic determinantal ideal

Burity, Ricardo; Miranda-Neto, Cleto

doi:10.1090/proc/15142

The module of logarithmic derivations of a generic determinantal ideal
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by Ricardo Burity and Cleto B. Miranda-Neto PDF

Proc. Amer. Math. Soc. 148 (2020), 4621-4634 Request permission

Abstract:

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 $P\subset R=K[\{X_{i,j}\}]$ generated by the maximal minors of an $(n+1)\times n$ generic matrix $(X_{i,j})$ over an arbitrary field $K$ with $n\geq 2$. 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.

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