The Likelihood Correspondence
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914278794067968 |
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| author | Kahle, Thomas Schenck, Hal Sturmfels, Bernd Wiesmann, Maximilian |
| author_facet | Kahle, Thomas Schenck, Hal Sturmfels, Bernd Wiesmann, Maximilian |
| contents | An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Laurent monomials in the equations of the smooth hypersurfaces. The family of these loci forms an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the minimal generators of the bihomogeneous prime ideal that defines this variety. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Likelihood Correspondence Kahle, Thomas Schenck, Hal Sturmfels, Bernd Wiesmann, Maximilian Commutative Algebra Algebraic Geometry Combinatorics Statistics Theory 13P25, 14M12, 62R01 (Primary) 13N05, 14J81 (Secondary) An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Laurent monomials in the equations of the smooth hypersurfaces. The family of these loci forms an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the minimal generators of the bihomogeneous prime ideal that defines this variety. |
| title | The Likelihood Correspondence |
| topic | Commutative Algebra Algebraic Geometry Combinatorics Statistics Theory 13P25, 14M12, 62R01 (Primary) 13N05, 14J81 (Secondary) |
| url | https://arxiv.org/abs/2503.02536 |