Counting points with Riemann-Roch formulas
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914693927403520 |
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| author | Martín-Morales, Jorge |
| author_facet | Martín-Morales, Jorge |
| contents | We provide an algorithm for computing the number of integral points lying in certain triangles that do not have integral vertices. We use techniques from Algebraic Geometry such as the Riemann-Roch formula for weighted projective planes and resolution of singularities. We analyze the complexity of the method and show that the worst case is given by the Fibonacci sequence. At the end of the manuscript a concrete example is developed in detail where the interplay with other invariants of singularity theory is also treated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting points with Riemann-Roch formulas Martín-Morales, Jorge Algebraic Geometry Computational Complexity 14B05, 32S45, 14H20, 14C40, 11P21 We provide an algorithm for computing the number of integral points lying in certain triangles that do not have integral vertices. We use techniques from Algebraic Geometry such as the Riemann-Roch formula for weighted projective planes and resolution of singularities. We analyze the complexity of the method and show that the worst case is given by the Fibonacci sequence. At the end of the manuscript a concrete example is developed in detail where the interplay with other invariants of singularity theory is also treated. |
| title | Counting points with Riemann-Roch formulas |
| topic | Algebraic Geometry Computational Complexity 14B05, 32S45, 14H20, 14C40, 11P21 |
| url | https://arxiv.org/abs/2402.18193 |