‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
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 &...
| Authors: | , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/225686 |
| Online Access: | https://hdl.handle.net/2445/225686 |
| Access Level: | Open access |
| Keyword: | Superfícies algebraiques Homologia Algebraic surfaces Homology |
| Summary: | 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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