2020/05/22 by Abdelmoubine Amar Henni, Henni, Abdelmoubine Amar
Mathematics · Physics and Astronomy · #14D20 #14F05 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2005.11291
openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \widetildeℙ3, 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 μ-stability. Furthermore, these sheaves will play a role in (partially) compactifying the t'Hooft component of the moduli space of instantons, on \widetildeℙ3. Finally, examples of these are shown to be smooth and smoothable.