The characteristic cycle of a non-confluent $\ell$-adic GKZ hypergeometric sheaf
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910539016306688 |
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| author | Liu, Peijiang |
| author_facet | Liu, Peijiang |
| contents | An $\ell$-adic GKZ hypergeometric sheaf is defined analogously to a GKZ hypergeometric $\mathcal{D}$-module. We introduce an algorithm of computing the characteristic cycle of an $\ell$-adic GKZ hypergeometric sheaf of certain type. Our strategy is to apply a formula of the characteristic cycle of the direct image of an $\ell$-adic sheaf. We verify the requirements for the formula to hold by calculating the dimension of the direct image of a certain closed conical subset of cotangent bundle. We also define an $\ell$-adic GKZ-type sheaf whose specialization tensored with a constant sheaf is isomorphic to an $\ell$-adic non-confluent GKZ hypergeometric sheaf. On the other hand, the topological model of an $\ell$-adic GKZ-type sheaf is isomorphic to the image by the de Rham functor of a non-confluent GKZ hypergeometric $\mathcal{D}$-module whose characteristic cycle has been calculated. This gives an easier way to determine the characteristic cycle of an $\ell$-adic non-confluent GKZ hypergeometric sheaf of certain type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The characteristic cycle of a non-confluent $\ell$-adic GKZ hypergeometric sheaf Liu, Peijiang Algebraic Geometry An $\ell$-adic GKZ hypergeometric sheaf is defined analogously to a GKZ hypergeometric $\mathcal{D}$-module. We introduce an algorithm of computing the characteristic cycle of an $\ell$-adic GKZ hypergeometric sheaf of certain type. Our strategy is to apply a formula of the characteristic cycle of the direct image of an $\ell$-adic sheaf. We verify the requirements for the formula to hold by calculating the dimension of the direct image of a certain closed conical subset of cotangent bundle. We also define an $\ell$-adic GKZ-type sheaf whose specialization tensored with a constant sheaf is isomorphic to an $\ell$-adic non-confluent GKZ hypergeometric sheaf. On the other hand, the topological model of an $\ell$-adic GKZ-type sheaf is isomorphic to the image by the de Rham functor of a non-confluent GKZ hypergeometric $\mathcal{D}$-module whose characteristic cycle has been calculated. This gives an easier way to determine the characteristic cycle of an $\ell$-adic non-confluent GKZ hypergeometric sheaf of certain type. |
| title | The characteristic cycle of a non-confluent $\ell$-adic GKZ hypergeometric sheaf |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.16381 |