The general ternary form can be recovered by its Hessian
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910870806724608 |
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| author | Ciliberto, Ciro Ottaviani, Giorgio Caro, Jerson Duque-Rosero, Juanita |
| author_facet | Ciliberto, Ciro Ottaviani, Giorgio Caro, Jerson Duque-Rosero, Juanita |
| contents | The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The general ternary form can be recovered by its Hessian Ciliberto, Ciro Ottaviani, Giorgio Caro, Jerson Duque-Rosero, Juanita Algebraic Geometry 14E05, 14H50, 14L30, 11D25, 14Q05 The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques. |
| title | The general ternary form can be recovered by its Hessian |
| topic | Algebraic Geometry 14E05, 14H50, 14L30, 11D25, 14Q05 |
| url | https://arxiv.org/abs/2406.05382 |