Classification of monads and a new moduli component of stable rank 2 bundles on $\mathbb{P}^3$ with even determinant and $c_2=9$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915041908883456 |
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| author | Fontes, Aislan Leal |
| author_facet | Fontes, Aislan Leal |
| contents | The goal of this paper is to classify all minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=0$ and $c_2=9$, with possible exception of two non-negative minimal monads, and thus we extend the classification of the minimal monads made by Hartshorne and Rao in \cite[Section 5.3]{HR91} when $c_2\leq8$. We also prove the existence of a new component of the moduli space $\mathcal{B}(9)$ which is distinct from the Hartshorne and Ein components. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_00043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of monads and a new moduli component of stable rank 2 bundles on $\mathbb{P}^3$ with even determinant and $c_2=9$ Fontes, Aislan Leal Algebraic Geometry 14D20, 14J10 The goal of this paper is to classify all minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=0$ and $c_2=9$, with possible exception of two non-negative minimal monads, and thus we extend the classification of the minimal monads made by Hartshorne and Rao in \cite[Section 5.3]{HR91} when $c_2\leq8$. We also prove the existence of a new component of the moduli space $\mathcal{B}(9)$ which is distinct from the Hartshorne and Ein components. |
| title | Classification of monads and a new moduli component of stable rank 2 bundles on $\mathbb{P}^3$ with even determinant and $c_2=9$ |
| topic | Algebraic Geometry 14D20, 14J10 |
| url | https://arxiv.org/abs/2412.00043 |