A Resolution of the Diagonal for Smooth Toric Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910839660871680 |
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| author | Anderson, Reginald |
| author_facet | Anderson, Reginald |
| contents | Beilinson gave a resolution of the diagonal for complex projective spaces, which Bayer-Popescu-Sturmfels generalized to what they refer to as unimodular projective toric varieties. The unimodular condition in Bayer-Popescu-Sturmfels' convention is more restrictive than being smooth. In the smooth, non-unimodular setting, extra vertices appear in the finite cellular complex which Bayer-Popescu-Sturmfels previously used to resolve the diagonal for unimodular projective toric varieties. We use the floor function to assign monomial labelings in a convex manner, and show that this assignment is compatible with the graded algebra involving the irrelevant ideal to give a resolution of the diagonal for a smooth projective toric variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09653 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Resolution of the Diagonal for Smooth Toric Varieties Anderson, Reginald Algebraic Geometry 14F08 Beilinson gave a resolution of the diagonal for complex projective spaces, which Bayer-Popescu-Sturmfels generalized to what they refer to as unimodular projective toric varieties. The unimodular condition in Bayer-Popescu-Sturmfels' convention is more restrictive than being smooth. In the smooth, non-unimodular setting, extra vertices appear in the finite cellular complex which Bayer-Popescu-Sturmfels previously used to resolve the diagonal for unimodular projective toric varieties. We use the floor function to assign monomial labelings in a convex manner, and show that this assignment is compatible with the graded algebra involving the irrelevant ideal to give a resolution of the diagonal for a smooth projective toric variety. |
| title | A Resolution of the Diagonal for Smooth Toric Varieties |
| topic | Algebraic Geometry 14F08 |
| url | https://arxiv.org/abs/2403.09653 |