2023/07/05 by Vincenzo Antonelli, Antonelli, Vincenzo, Francesco Malaspina +5
Mathematics · #14D21 #14J45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 14J60. Secondary: 14F06
paper · pdf · doi:10.48550/arxiv.2307.02197
openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we study the moduli spaces of instanton bundles on the flag twistor space F:=F(0,1,2). We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on F. In particular we prove that there exist μ-stable 't Hooft bundles for each admissible charge k. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge k. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in F as well as the family of del Pezzo surfaces realized as hyperplane sections of F. Finally we investigate the splitting behaviour of 't Hooft bundles when restricted to conics.