(Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911404731138048 |
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| author | Brüser, Clemens Kummer, Mario |
| author_facet | Brüser, Clemens Kummer, Mario |
| contents | We prove that every real nonnegative ternary quartic whose complex zero set is smooth can be represented as the determinant of a symmetric matrix with quadratic entries which is everywhere positive semidefinite. We show that the corresponding statement fails for the Robinson polynomial, answering a question by Buckley and Šivic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial Brüser, Clemens Kummer, Mario Algebraic Geometry 14P99, 14Q30 (Primary) We prove that every real nonnegative ternary quartic whose complex zero set is smooth can be represented as the determinant of a symmetric matrix with quadratic entries which is everywhere positive semidefinite. We show that the corresponding statement fails for the Robinson polynomial, answering a question by Buckley and Šivic. |
| title | (Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial |
| topic | Algebraic Geometry 14P99, 14Q30 (Primary) |
| url | https://arxiv.org/abs/2412.02319 |