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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.
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
Full Text: DOI
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