H-Instanton Bundles on Three-Dimensional Smooth Toric Varieties with Picard Number Two
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914311851474944 |
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| author | Genc, Ozhan Malaspina, Francesco |
| author_facet | Genc, Ozhan Malaspina, Francesco |
| contents | We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of $H$-instanton bundles on $X_e$, generalizing the classical monads on $\mathbb P^3$. We then characterize $H$-instanton bundles with second Chern class supported in a single degree, and investigate their existence and moduli spaces. Finally, for $e\leq 3$, we prove the existence of $H$-instanton bundles for all admissible second Chern classes. These results extend previous constructions on specific cases and contribute to the study of instanton bundles on threefolds with higher Picard number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | H-Instanton Bundles on Three-Dimensional Smooth Toric Varieties with Picard Number Two Genc, Ozhan Malaspina, Francesco Algebraic Geometry 14F05, 14J60 We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of $H$-instanton bundles on $X_e$, generalizing the classical monads on $\mathbb P^3$. We then characterize $H$-instanton bundles with second Chern class supported in a single degree, and investigate their existence and moduli spaces. Finally, for $e\leq 3$, we prove the existence of $H$-instanton bundles for all admissible second Chern classes. These results extend previous constructions on specific cases and contribute to the study of instanton bundles on threefolds with higher Picard number. |
| title | H-Instanton Bundles on Three-Dimensional Smooth Toric Varieties with Picard Number Two |
| topic | Algebraic Geometry 14F05, 14J60 |
| url | https://arxiv.org/abs/2602.07155 |