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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
Software:
Macaulay2
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