Singular locus of instanton sheaves on ${\mathbb{P}}^3$

Abstract

We prove that the singular locus of a rank 2 instanton sheaf $E$ on ${\mathbb{P}}^3$ which is not locally free has pure dimension 1. Moreover, we also show that the dual and double dual of $E$ are isomorphic locally free instanton sheaves, and that the sheaves $\mathcal{E}xt^1(E,\mathcal{O}_{\mathbb{P}^3)$ and $E^{\vee \vee }/E$ are rank $0$ instantons. We also provide explicit examples of instanton sheaves of rank $3$ and $4$ illustrating that all of these claims are false for higher rank instanton sheaves.

14 pages

Cited by in corpus (5)

• Moduli spaces of rank 2 instanton sheaves on the projective space
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• Instanton sheaves and representations of quivers
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$
• Instanton Sheaves on Ruled Fano 3-folds of Picard Rank 2 and Index 1