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A family of reflexive vector bundles of reduction number one. (English) Zbl 1423.13045
Modules (reflexive vector bundles) having prescribed reduction number $$r\geq 1$$ and good properties for the Rees algebra are studied. In particular, the case $$r=1$$ is considered. The author shows 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.
##### MSC:
 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13C14 Cohen-Macaulay modules 13C40 Linkage, complete intersections and determinantal ideals
##### Keywords:
modules; vector bundles
Macaulay2
Full Text:
##### References:
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