2025/01/31 by Mihai Halic, Halic, Mihai, Roshan Tajarod +1
Mathematics · #14D20 #14D21 #14J60 #14M20 #53C07 #Algebraic Geometry (math.AG) #FOS: Mathematics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2501.19189
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on \mathbb P3. In particular, the result applies to the rank-2 case. This problem was first studied by Barth, Ellingsrud-Stromme, Hartshorne, Hirschowitz-Narasimhan in the late 1970s. We also show that the mathematical instantons of variable rank and charge form a monoidal category. The proof is based on an in-depth analysis of the Barth-Hulek monad-construction and on a detailed description of the moduli space of (framed and unframed) stable bundles on Hirzebruch surfaces.