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.
‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons / Antonelli, Vincenzo; Malaspina, Francesco; Marchesi, Simone; Pons-Llopis, Juan. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - ELETTRONICO. - 202:(2025), pp. 1-44. [10.1016/j.matpur.2025.103763]
‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
Antonelli, Vincenzo;Malaspina, Francesco;Pons-Llopis, Juan
2025
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.File | Dimensione | Formato | |
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tHooftFlag.pdf
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https://hdl.handle.net/11583/3001147