‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons

Abstract

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 mu -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 behavior of 't Hooft bundles when restricted to conics.