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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.14628 |
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| _version_ | 1866908836434018304 |
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| author | Pokidkin, Vladislav |
| author_facet | Pokidkin, Vladislav |
| contents | In the space of square matrices, we characterize row-generated subspaces, on which the determinant is an irreducible polynomial. As a corollary, we characterize square systems of polynomial equations with indeterminate coefficients, whose discriminant is an irreducible hypersurface. This resolves a conjecture of Esterov, and, in a sequel paper, leads to a complete description of components and codimensions for discriminants of square systems of equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducibility of determinants, and Esterov's conjecture on $\mathscr{A}$-discriminants Pokidkin, Vladislav Algebraic Geometry Combinatorics In the space of square matrices, we characterize row-generated subspaces, on which the determinant is an irreducible polynomial. As a corollary, we characterize square systems of polynomial equations with indeterminate coefficients, whose discriminant is an irreducible hypersurface. This resolves a conjecture of Esterov, and, in a sequel paper, leads to a complete description of components and codimensions for discriminants of square systems of equations. |
| title | Irreducibility of determinants, and Esterov's conjecture on $\mathscr{A}$-discriminants |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2501.14628 |