A family of reflexive vector bundles of reduction number one

  • Cleto B. Miranda-Neto


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.


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How to Cite
Miranda-Neto, C. (2019). A family of reflexive vector bundles of reduction number one. MATHEMATICA SCANDINAVICA, 124(2), 188-202. https://doi.org/10.7146/math.scand.a-111889