Saito criterion and its avatars
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913433567363072 |
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| author | Faenzi, Daniele Jardim, Marcos Vallès, Jean |
| author_facet | Faenzi, Daniele Jardim, Marcos Vallès, Jean |
| contents | Saito gave a nice and efficient criterion to determine whether the module of logarithmic derivation associated with a reduced divisor in a complex variety is free or not. The aim of this note is to propose a new proof of this criterion, in the affine space, in the projective space, and for multiderivations, based on straightforward observations concerning free and reflexive modules. This point of view also allows us to prove a generalized version of the Saito criterion that applies to derivation modules associated with several polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Saito criterion and its avatars Faenzi, Daniele Jardim, Marcos Vallès, Jean Algebraic Geometry Saito gave a nice and efficient criterion to determine whether the module of logarithmic derivation associated with a reduced divisor in a complex variety is free or not. The aim of this note is to propose a new proof of this criterion, in the affine space, in the projective space, and for multiderivations, based on straightforward observations concerning free and reflexive modules. This point of view also allows us to prove a generalized version of the Saito criterion that applies to derivation modules associated with several polynomials. |
| title | Saito criterion and its avatars |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2402.08305 |