Birational zeta functions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915477854355456 |
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| author | Biesbrouck, Tom Budur, Nero Nicaise, Johannes Veys, Willem |
| author_facet | Biesbrouck, Tom Budur, Nero Nicaise, Johannes Veys, Willem |
| contents | We define a birational analog of the motivic zeta function of a reduced polynomial in terms of minimal models. It admits an intrinsic meaning in terms of contact loci of arcs, an analog of a result of Denef and Loeser in the motivic case. We show that for local plane curve singularities the poles of the birational zeta function essentially coincide with the poles of the motivic zeta function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Birational zeta functions Biesbrouck, Tom Budur, Nero Nicaise, Johannes Veys, Willem Algebraic Geometry We define a birational analog of the motivic zeta function of a reduced polynomial in terms of minimal models. It admits an intrinsic meaning in terms of contact loci of arcs, an analog of a result of Denef and Loeser in the motivic case. We show that for local plane curve singularities the poles of the birational zeta function essentially coincide with the poles of the motivic zeta function. |
| title | Birational zeta functions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.03352 |