Moduli spaces of sheaves via affine Grassmannians
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866913219912663040 |
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| author | Halpern-Leistner, Daniel Herrero, Andres Fernandez Jones, Trevor |
| author_facet | Halpern-Leistner, Daniel Herrero, Andres Fernandez Jones, Trevor |
| contents | We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two familiar moduli problems: the stack of $Λ$-modules and the stack of pairs. In both examples, we construct a $Θ$-stratification of the stack, defined in terms of a polynomial numerical invariant, and we construct good moduli spaces for the open substacks of semistable points. One of the essential ingredients is the construction of higher dimensional analogues of the affine Grassmannian for the moduli problems considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_02172 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Moduli spaces of sheaves via affine Grassmannians Halpern-Leistner, Daniel Herrero, Andres Fernandez Jones, Trevor Algebraic Geometry 14D23 (Primary) 14J60, 14F06, 14L24 (Secondary) We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two familiar moduli problems: the stack of $Λ$-modules and the stack of pairs. In both examples, we construct a $Θ$-stratification of the stack, defined in terms of a polynomial numerical invariant, and we construct good moduli spaces for the open substacks of semistable points. One of the essential ingredients is the construction of higher dimensional analogues of the affine Grassmannian for the moduli problems considered. |
| title | Moduli spaces of sheaves via affine Grassmannians |
| topic | Algebraic Geometry 14D23 (Primary) 14J60, 14F06, 14L24 (Secondary) |
| url | https://arxiv.org/abs/2107.02172 |