Sheaf stable pairs on projective surfaces and birational geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918268587999232 |
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| author | Birkar, Caucher Jia, Jia Sheshmani, Artan Wang, Chengxi |
| author_facet | Birkar, Caucher Jia, Jia Sheshmani, Artan Wang, Chengxi |
| contents | We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth projective surface. Having fixed the Chern character of E, the resulting moduli space is isomorphic to some subscheme of the Quot-scheme parametrising quotient sheaves of appropriate Chern character. We establish a connection between moduli space of higher rank stable pairs and stable minimal models induced by the sheaf E and sections s_i and the relative lc model of base surface, and use birational geometry of minimal models to analyse in detail the components of the fibre of the Hilbert-Chow morphism from the moduli space to the Hilbert scheme of effective Cartier divisors on the base surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sheaf stable pairs on projective surfaces and birational geometry Birkar, Caucher Jia, Jia Sheshmani, Artan Wang, Chengxi Algebraic Geometry 14J10, 14E30, 14H60 We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth projective surface. Having fixed the Chern character of E, the resulting moduli space is isomorphic to some subscheme of the Quot-scheme parametrising quotient sheaves of appropriate Chern character. We establish a connection between moduli space of higher rank stable pairs and stable minimal models induced by the sheaf E and sections s_i and the relative lc model of base surface, and use birational geometry of minimal models to analyse in detail the components of the fibre of the Hilbert-Chow morphism from the moduli space to the Hilbert scheme of effective Cartier divisors on the base surface. |
| title | Sheaf stable pairs on projective surfaces and birational geometry |
| topic | Algebraic Geometry 14J10, 14E30, 14H60 |
| url | https://arxiv.org/abs/2601.00153 |