Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$
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| Format: | Preprint |
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2024
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| _version_ | 1866911935649284096 |
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| author | Fontes, Aislan Jardim, Marcos |
| author_facet | Fontes, Aislan Jardim, Marcos |
| contents | In this paper, we provide a complete classification of the positive minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=-1, c_2=10$ and we prove the existence of a new irreducible component of the moduli space $\mathcal{B}(-1,10)$ of a rank 2 stable bundles with the given Chern classes. We also show that Hartshorne's conditions on a sequence $\mathcal{X}$ of 10 integers are sufficient and necessary for the existence of a stable rank 2 bundle with odd determinant and spectrum $\mathcal{X}$. Furthermore, we prove that the sequence of integers $\{-2^{n-1},-1,0,1^{n-1}\}$ for $ n\geq4$ is realized as the spectrum of a stable rank 2 bundle $\EE$ of odd determinant by computing the minimal generators of its Rao module. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_19505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$ Fontes, Aislan Jardim, Marcos Algebraic Geometry In this paper, we provide a complete classification of the positive minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=-1, c_2=10$ and we prove the existence of a new irreducible component of the moduli space $\mathcal{B}(-1,10)$ of a rank 2 stable bundles with the given Chern classes. We also show that Hartshorne's conditions on a sequence $\mathcal{X}$ of 10 integers are sufficient and necessary for the existence of a stable rank 2 bundle with odd determinant and spectrum $\mathcal{X}$. Furthermore, we prove that the sequence of integers $\{-2^{n-1},-1,0,1^{n-1}\}$ for $ n\geq4$ is realized as the spectrum of a stable rank 2 bundle $\EE$ of odd determinant by computing the minimal generators of its Rao module. |
| title | Classification of monads and moduli components of stable rank 2 bundles with odd determinant and $c_2=10$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.19505 |