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\(p\)-Buchsbaum rank \(2\) bundles on the projective space. (English) Zbl 1346.14110
A rank \(2\) bundle \(E\) on \(\mathbb P^3\) is \(p\)-Buchsbaum when \(p\) is the minimum such that the multiplication by \(H^\oplus(\mathcal O(p))\) annihilates the cohomology module \(H_*^1(E)\). When \(p=0,1,2\), the classification of \(p\)-Buchsbaum bundles is known. In particular, \(2\)-Buchsbaum bundles are instanton bundles of charge \(2\). In the paper under review, the authors prove that, conversely, every instanton bundle of charge \(k\) is \(p\)-Buchsbaum for some \(p\leq k\). The authors also provide an example of a \(3\)-Buchsbaum bundle which is not an instanton bundle.
MSC:
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
Keywords:
vector bundles
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