Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912359710195712 |
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| author | Halic, Mihai Tajarod, Roshan |
| author_facet | Halic, Mihai Tajarod, Roshan |
| contents | We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by Barth, Ellingsrud-Stromme, Hartshorne, Hirschowitz-Narasimhan in the late 1970s. We also show that the mathematical instantons of variable rank and charge form a monoidal category. The proof is based on an in-depth analysis of the Barth-Hulek monad-construction and on a detailed description of the moduli space of (framed and unframed) stable bundles on Hirzebruch surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space Halic, Mihai Tajarod, Roshan Algebraic Geometry 14M20, 14D20, 14J60, 14D21, 53C07 We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by Barth, Ellingsrud-Stromme, Hartshorne, Hirschowitz-Narasimhan in the late 1970s. We also show that the mathematical instantons of variable rank and charge form a monoidal category. The proof is based on an in-depth analysis of the Barth-Hulek monad-construction and on a detailed description of the moduli space of (framed and unframed) stable bundles on Hirzebruch surfaces. |
| title | Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space |
| topic | Algebraic Geometry 14M20, 14D20, 14J60, 14D21, 53C07 |
| url | https://arxiv.org/abs/2501.19189 |