't Hooft bundles on the complete flag threefold and moduli spaces of instantons
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915286731456512 |
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| author | Antonelli, Vincenzo Malaspina, Francesco Marchesi, Simone Pons-Llopis, Joan |
| author_facet | Antonelli, Vincenzo Malaspina, Francesco Marchesi, Simone Pons-Llopis, Joan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02197 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 't Hooft bundles on the complete flag threefold and moduli spaces of instantons Antonelli, Vincenzo Malaspina, Francesco Marchesi, Simone Pons-Llopis, Joan Algebraic Geometry Primary: 14J60. Secondary: 14F06, 14J45, 14D21 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. |
| title | 't Hooft bundles on the complete flag threefold and moduli spaces of instantons |
| topic | Algebraic Geometry Primary: 14J60. Secondary: 14F06, 14J45, 14D21 |
| url | https://arxiv.org/abs/2307.02197 |