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A Horrocks’ theorem for reflexive sheaves. (English) Zbl 06845880
Summary: In this paper, we define $$m$$-tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology. We prove that the rank of any $$m$$-tail reflexive sheaf $$\mathcal{E}$$ on $$\mathbb{P}^n$$ is greater or equal to $$n m - m$$. We completely describe $$m$$-tail reflexive sheaves on $$\mathbb{P}^n$$ of minimal rank and we construct huge families of $$m$$-tail reflexive sheaves of higher rank.
##### MSC:
 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
##### Keywords:
reflexive sheaves; cohomology
Macaulay2
Full Text:
##### References:
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