A family of reflexive vector bundles of reduction number one - Miranda-Neto, Cleto B. (MATHEMATICA SCANDINAVICA, 2019)
A difficult issue in modern commutative algebra asks for examples of modules (more interestingly, reflexive vector bundles) having prescribed reduction number r≥ 1. The problem is even subtler if in addition we are interested in good properties for the Rees algebra. In this note we consider the case r=1. Precisely, we show that the module of logarithmic vector fields of the Fermat divisor of any degree in projective 3-space is a reflexive vector bundle of reduction number 1 and Gorenstein Rees ring.