Logarithmic vector fields and foliations on toric varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909291657560064 |
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| author | Faenzi, Daniele Jardim, Marcos Montoya, William D |
| author_facet | Faenzi, Daniele Jardim, Marcos Montoya, William D |
| contents | We introduce a toric version of the sheaf of logarithmic vector fields along a divisor of a simplicial toric variety. The notion is also relevant for algebraically independent families of polynomials in the Cox ring. We provide a generalisation of the Saito criterion for the freeness of the toric logarithmic sheaf. We explain the relationship between this sheaf and the usual sheaf of logarithmic vector fields and the connection with holomorphic foliations on toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic vector fields and foliations on toric varieties Faenzi, Daniele Jardim, Marcos Montoya, William D Algebraic Geometry We introduce a toric version of the sheaf of logarithmic vector fields along a divisor of a simplicial toric variety. The notion is also relevant for algebraically independent families of polynomials in the Cox ring. We provide a generalisation of the Saito criterion for the freeness of the toric logarithmic sheaf. We explain the relationship between this sheaf and the usual sheaf of logarithmic vector fields and the connection with holomorphic foliations on toric varieties. |
| title | Logarithmic vector fields and foliations on toric varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.10671 |