A Hessian criterion for totally positive Toeplitz matrices and a new proof of Cattani's theorem in two variables
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912493155123200 |
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| author | McDaniel, Chris |
| author_facet | McDaniel, Chris |
| contents | Cattani's theorem for graded Artinian Gorenstein algebras states that the ordinary Hodge-Riemann relations imply the mixed Hodge-Riemann relations under certain conditions. We give a new proof of this result for codimension two algebras. Our proof leads to a Hessian criterion for totally positive Toeplitz matrices, which is analogous to the Wronskian criterion for totally positive flags discovered recently by S. Karp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hessian criterion for totally positive Toeplitz matrices and a new proof of Cattani's theorem in two variables McDaniel, Chris Commutative Algebra Cattani's theorem for graded Artinian Gorenstein algebras states that the ordinary Hodge-Riemann relations imply the mixed Hodge-Riemann relations under certain conditions. We give a new proof of this result for codimension two algebras. Our proof leads to a Hessian criterion for totally positive Toeplitz matrices, which is analogous to the Wronskian criterion for totally positive flags discovered recently by S. Karp. |
| title | A Hessian criterion for totally positive Toeplitz matrices and a new proof of Cattani's theorem in two variables |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2507.15043 |