Stable toric sheaves. I : Chern classes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914140053831680 |
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| author | Tipler, Carl |
| author_facet | Tipler, Carl |
| contents | We study rank 2 torus-equivariant torsion-free sheaves on the complex projective space. For reflexive sheaves we derive a simple formula for the Chern polynomial, and in the general torsion-free case we introduce an iterative construction method based on elementary injections, allowing us to prescribe Chern classes. This yields infinite families of explicit examples on $\mathbb{P}^4$ and $\mathbb{P}^5$, and establishes existence on $\mathbb{P}^n$ for all $n\geq 3$, with Chern classes satisfying all known constraints arising from locally freeness and indecomposability. We also provide simple obstructions for smoothability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable toric sheaves. I : Chern classes Tipler, Carl Algebraic Geometry 14M07 (Primary) 14M25 (Secondary) We study rank 2 torus-equivariant torsion-free sheaves on the complex projective space. For reflexive sheaves we derive a simple formula for the Chern polynomial, and in the general torsion-free case we introduce an iterative construction method based on elementary injections, allowing us to prescribe Chern classes. This yields infinite families of explicit examples on $\mathbb{P}^4$ and $\mathbb{P}^5$, and establishes existence on $\mathbb{P}^n$ for all $n\geq 3$, with Chern classes satisfying all known constraints arising from locally freeness and indecomposability. We also provide simple obstructions for smoothability. |
| title | Stable toric sheaves. I : Chern classes |
| topic | Algebraic Geometry 14M07 (Primary) 14M25 (Secondary) |
| url | https://arxiv.org/abs/2510.14651 |