Decomposing Determinantal Varieties from Statistics via Matroid Theory
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arXiv
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| Format: | Preprint |
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2026
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| author | Alexandersson, Per Alexandr, Yulia Liwski, Emiliano Mohammadi, Fatemeh Semnani, Pardis |
| author_facet | Alexandersson, Per Alexandr, Yulia Liwski, Emiliano Mohammadi, Fatemeh Semnani, Pardis |
| contents | We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases. Each variety encodes a collection of matroids, whose flats capture algebraic dependencies among variables. Using this approach, we provide a systematic description of the components, their dimensions, and defining equations, and introduce a combinatorial framework for computing the degree of the determinantal variety. Our approach highlights the central role of matroidal structures in the study of determinantal varieties and extends beyond the reach of current computational techniques. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15128 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decomposing Determinantal Varieties from Statistics via Matroid Theory Alexandersson, Per Alexandr, Yulia Liwski, Emiliano Mohammadi, Fatemeh Semnani, Pardis Combinatorics Commutative Algebra Algebraic Geometry Statistics Theory 14M12, 13P10, 14A10, 05B35, 62R01 We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases. Each variety encodes a collection of matroids, whose flats capture algebraic dependencies among variables. Using this approach, we provide a systematic description of the components, their dimensions, and defining equations, and introduce a combinatorial framework for computing the degree of the determinantal variety. Our approach highlights the central role of matroidal structures in the study of determinantal varieties and extends beyond the reach of current computational techniques. |
| title | Decomposing Determinantal Varieties from Statistics via Matroid Theory |
| topic | Combinatorics Commutative Algebra Algebraic Geometry Statistics Theory 14M12, 13P10, 14A10, 05B35, 62R01 |
| url | https://arxiv.org/abs/2601.15128 |