Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918249244917760 |
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| author | Maraj, Aida Pal, Arpan |
| author_facet | Maraj, Aida Pal, Arpan |
| contents | The motivation for this paper is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated to V. If the dimension of V is strictly less than the dimension of the above mentioned objects, then V is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to provide examples of non-toric statistical models in algebraic statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10741 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics Maraj, Aida Pal, Arpan Algebraic Geometry Statistics Theory 62R01, 17B45, 14Q20, 14-04 The motivation for this paper is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated to V. If the dimension of V is strictly less than the dimension of the above mentioned objects, then V is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to provide examples of non-toric statistical models in algebraic statistics. |
| title | Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics |
| topic | Algebraic Geometry Statistics Theory 62R01, 17B45, 14Q20, 14-04 |
| url | https://arxiv.org/abs/2309.10741 |