Deformations and Simultaneous Resolution of Determinantal Surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915587348758528 |
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| author | Makonzi, Brian |
| author_facet | Makonzi, Brian |
| contents | This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain noncommutative relations, namely those of the canonical algebra of Ringel, are required. All the relations of the reconstruction algebra except the canonical relation are then deformed, and these deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02982 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformations and Simultaneous Resolution of Determinantal Surfaces Makonzi, Brian Algebraic Geometry Representation Theory 14D15, 14J17 This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain noncommutative relations, namely those of the canonical algebra of Ringel, are required. All the relations of the reconstruction algebra except the canonical relation are then deformed, and these deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. |
| title | Deformations and Simultaneous Resolution of Determinantal Surfaces |
| topic | Algebraic Geometry Representation Theory 14D15, 14J17 |
| url | https://arxiv.org/abs/2309.02982 |