Nonstable reflexive sheaves on 𝑃³

Sauer, Timothy

doi:10.1090/S0002-9947-1984-0722766-9

Nonstable reflexive sheaves on $\textbf {P}^{3}$
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Trans. Amer. Math. Soc. 281 (1984), 633-655 Request permission

Abstract:

The spectrum is defined for nonstable rank two reflexive sheaves on ${{\mathbf {P}}^3}$ and is used to establish vanishing theorems for intermediate cohomology in terms of the Chern classes and the order of nonstability. These results are shown to be best possible and the extremal cases are classified. Some applications to Cohen-Macaulay generically local complete intersection curves in ${{\mathbf {P}}^3}$ are given.

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