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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)
vector bundles
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