Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^3$ at a point

Abstract

We consider an extension of the instanton bundles definition, given by Casnati-Coskun-Genk-Malaspina, for Fano threefolds, in order to include non locally-free ones on the blow-up $\widetilde{{\mathbb{P}}^3},$ of the projective $3-$space at a point. With the proposed definition, we prove that any reflexive instanton sheaf must be locally free, and that the strictly torsion free instanton sheaves have singularities of pure dimension $1.$ We construct examples and study their $\mu -$stability. Furthermore, these sheaves will play a role in (partially) compactifying the t'Hooft component of the moduli space of instantons, on $\widetilde{{\mathbb{P}}^3}.$ Finally, examples of these are shown to be smooth and smoothable.

22pages

References in corpus (3)

• Rational curves and instantons on the Fano threefold $Y_5$
• Irreducible components of the moduli space of rank 2 sheaves of odd determinant on the projective space
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$