Some moduli spaces of $α$-stable coherent systems on algebraic surfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915877215010816 |
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| author | Costa, L. Tarrío, I. Macías Roa-Leguizamón, L. |
| author_facet | Costa, L. Tarrío, I. Macías Roa-Leguizamón, L. |
| contents | Let $X$ be a smooth, irreducible, projective algebraic surface, and let $α\in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $α$-stable coherent systems of type $(n; c_{1}, c_{2}, k)$ with $k < n$ on $X$, for sufficiently large values of $α$. We prove that, for $α$ sufficiently large, the moduli space admits a description as a Grassmann bundle over a moduli space of $H$-stable torsion free sheaves. As a consequence, we obtain results on irreducibility, dimension. Our approach relies on establishing a correspondence between $α$-stable coherent systems and extensions of $H$-stable torsion free sheaves by trivial bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some moduli spaces of $α$-stable coherent systems on algebraic surfaces Costa, L. Tarrío, I. Macías Roa-Leguizamón, L. Algebraic Geometry 14J60, 14D20, 14H60 Let $X$ be a smooth, irreducible, projective algebraic surface, and let $α\in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $α$-stable coherent systems of type $(n; c_{1}, c_{2}, k)$ with $k < n$ on $X$, for sufficiently large values of $α$. We prove that, for $α$ sufficiently large, the moduli space admits a description as a Grassmann bundle over a moduli space of $H$-stable torsion free sheaves. As a consequence, we obtain results on irreducibility, dimension. Our approach relies on establishing a correspondence between $α$-stable coherent systems and extensions of $H$-stable torsion free sheaves by trivial bundles. |
| title | Some moduli spaces of $α$-stable coherent systems on algebraic surfaces |
| topic | Algebraic Geometry 14J60, 14D20, 14H60 |
| url | https://arxiv.org/abs/2511.16581 |