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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2110.02218 |
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| _version_ | 1866915296729628672 |
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| author | García, Darío Rizzo, Pedro del Valle, Joel Torres |
| author_facet | García, Darío Rizzo, Pedro del Valle, Joel Torres |
| contents | In this work we propose a notion of genus in the context of Zariski geometries and we obtain natural generalizations of the Riemann--Hurwitz Theorem and the Hurwitz Theorem in the context of very ample Zariski geometries. As a corollary, we show that such notion of genus cannot be first-order definable in the full language of a Zariski geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_02218 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A note on the definability of genus for Zariski geometries García, Darío Rizzo, Pedro del Valle, Joel Torres Logic Algebraic Geometry In this work we propose a notion of genus in the context of Zariski geometries and we obtain natural generalizations of the Riemann--Hurwitz Theorem and the Hurwitz Theorem in the context of very ample Zariski geometries. As a corollary, we show that such notion of genus cannot be first-order definable in the full language of a Zariski geometry. |
| title | A note on the definability of genus for Zariski geometries |
| topic | Logic Algebraic Geometry |
| url | https://arxiv.org/abs/2110.02218 |