Commutative Algebra and Algebraic Geometry using OSCAR
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909174213902336 |
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| author | Boehm, Janko Decker, Wolfram Schreyer, Frank-Olaf |
| author_facet | Boehm, Janko Decker, Wolfram Schreyer, Frank-Olaf |
| contents | We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the computation of syzygies, then apply these techniques to deal with ideal and ring theoretic concepts such as primary decomposition and normalization, and finally use them for geometric case studies which concern curves and surfaces, both from a local and global point of view. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commutative Algebra and Algebraic Geometry using OSCAR Boehm, Janko Decker, Wolfram Schreyer, Frank-Olaf Algebraic Geometry Commutative Algebra 14Qxx, 13P10, 13D02 (Primary), 14H50, 14Jxx, 14F05, 14Dxx, 14C30, 14D15 (Secondary) We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to Groebner basis techniques, with particular emphasis on the computation of syzygies, then apply these techniques to deal with ideal and ring theoretic concepts such as primary decomposition and normalization, and finally use them for geometric case studies which concern curves and surfaces, both from a local and global point of view. |
| title | Commutative Algebra and Algebraic Geometry using OSCAR |
| topic | Algebraic Geometry Commutative Algebra 14Qxx, 13P10, 13D02 (Primary), 14H50, 14Jxx, 14F05, 14Dxx, 14C30, 14D15 (Secondary) |
| url | https://arxiv.org/abs/2404.12085 |