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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01379 |
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| _version_ | 1866917767261716480 |
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| author | Suter, Aiden Webster, Ben |
| author_facet | Suter, Aiden Webster, Ben |
| contents | Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities.
In this paper, we give a concrete construction of this tilting generator on the cotangent bundle of $Gr(2,4)$, the Grassmannian of 2-planes in $\mathbb{C}^4$. This construction builds on work of the second author describing these tilting bundles in terms of KLRW algebras, but in this low-dimensional case, we are able to describe our tilting generator as a sum of geometrically natural bundles on $T^*Gr(2,4)$: line bundles and their extensions, as well as the tautological bundle and its perpendicular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch Suter, Aiden Webster, Ben Algebraic Geometry Representation Theory Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities. In this paper, we give a concrete construction of this tilting generator on the cotangent bundle of $Gr(2,4)$, the Grassmannian of 2-planes in $\mathbb{C}^4$. This construction builds on work of the second author describing these tilting bundles in terms of KLRW algebras, but in this low-dimensional case, we are able to describe our tilting generator as a sum of geometrically natural bundles on $T^*Gr(2,4)$: line bundles and their extensions, as well as the tautological bundle and its perpendicular. |
| title | Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2409.01379 |