Sampling Algebra Structures on Minimal Free Resolutions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917785647448064 |
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| author | Christensen, Lars Winther Gotchey, Orin Hardesty, Alexis |
| author_facet | Christensen, Lars Winther Gotchey, Orin Hardesty, Alexis |
| contents | Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually occur; this realizability question was formally raised by Avramov in 2012. We discuss the outcomes of an experiment performed to shed light on Avramov's question: Using the computer algebra system Macaulay2, we classify a billion randomly generated ideals and build a database with examples of ideals of all classes realized in the experiment. Based on the outcomes, we discuss the status of recent conjectures that relate to the realizability question. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_13687 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sampling Algebra Structures on Minimal Free Resolutions Christensen, Lars Winther Gotchey, Orin Hardesty, Alexis Commutative Algebra Primary: 13-11. Secondary: 13C05, 13D02 Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually occur; this realizability question was formally raised by Avramov in 2012. We discuss the outcomes of an experiment performed to shed light on Avramov's question: Using the computer algebra system Macaulay2, we classify a billion randomly generated ideals and build a database with examples of ideals of all classes realized in the experiment. Based on the outcomes, we discuss the status of recent conjectures that relate to the realizability question. |
| title | Sampling Algebra Structures on Minimal Free Resolutions |
| topic | Commutative Algebra Primary: 13-11. Secondary: 13C05, 13D02 |
| url | https://arxiv.org/abs/2303.13687 |