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

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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.

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Journal de Mathématiques Pures et Appliquées, 2025, vol. 202

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cc-by (c) Vincenzo Antonelli et al., 2025

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Articles publicats en revistes (Matemàtiques i Informàtica)

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