TY - JOUR AU - Miranda-Neto, Cleto B. PY - 2019/06/17 Y2 - 2024/03/29 TI - A family of reflexive vector bundles of reduction number one JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 124 IS - 2 SE - Articles DO - 10.7146/math.scand.a-111889 UR - https://www.mscand.dk/article/view/111889 SP - 188-202 AB - <p>A difficult issue in modern commutative algebra asks for examples of modules (more interestingly, reflexive vector bundles) having prescribed reduction number $r\geq 1$. 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.</p> ER -