Modular Serre Correspondence via stable pairs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915717582946304 |
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| author | Jardim, Marcos Mu, Dapeng |
| author_facet | Jardim, Marcos Mu, Dapeng |
| contents | A stable pair on a projective variety consists of a sheaf and a global section subject to stability conditions parameterized by rational polynomials. We will show that for a smooth projective threefold and a class of a rank 2 sheaf, there are two stability chambers (in the space of rational polynomials under the lexicographic order) for which the moduli spaces of semistable pairs admit morphisms to a Gieseker moduli space of rank 2 semistable sheaves and a Hilbert scheme, respectively. In the latter moduli space, every semistable pair corresponds to a closed sub-scheme of codimension 2 with an extension class, providing a generalization of the Serre correspondence. These two moduli spaces are related by finitely many wall-crossings. We provide explicit descriptions of those wall-crossings for certain fixed numerical classes. In particular, these wall-crossings preserve the connectedness of the moduli space of semistable pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular Serre Correspondence via stable pairs Jardim, Marcos Mu, Dapeng Algebraic Geometry A stable pair on a projective variety consists of a sheaf and a global section subject to stability conditions parameterized by rational polynomials. We will show that for a smooth projective threefold and a class of a rank 2 sheaf, there are two stability chambers (in the space of rational polynomials under the lexicographic order) for which the moduli spaces of semistable pairs admit morphisms to a Gieseker moduli space of rank 2 semistable sheaves and a Hilbert scheme, respectively. In the latter moduli space, every semistable pair corresponds to a closed sub-scheme of codimension 2 with an extension class, providing a generalization of the Serre correspondence. These two moduli spaces are related by finitely many wall-crossings. We provide explicit descriptions of those wall-crossings for certain fixed numerical classes. In particular, these wall-crossings preserve the connectedness of the moduli space of semistable pairs. |
| title | Modular Serre Correspondence via stable pairs |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.08480 |