A proof of the Brill-Noether method from scratch
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929509983322112 |
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| author | Berardini, Elena Couvreur, Alain Lecerf, Grégoire |
| author_facet | Berardini, Elena Couvreur, Alain Lecerf, Grégoire |
| contents | In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely on abstract concepts of algebraic geometry and commutative algebra. In this paper we present a short self-contained and elementary proof that mostly needs Newton polygons, Hensel lifting, bivariate resultants, and Chinese remaindering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12725 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A proof of the Brill-Noether method from scratch Berardini, Elena Couvreur, Alain Lecerf, Grégoire Algebraic Geometry Symbolic Computation In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely on abstract concepts of algebraic geometry and commutative algebra. In this paper we present a short self-contained and elementary proof that mostly needs Newton polygons, Hensel lifting, bivariate resultants, and Chinese remaindering. |
| title | A proof of the Brill-Noether method from scratch |
| topic | Algebraic Geometry Symbolic Computation |
| url | https://arxiv.org/abs/2208.12725 |