The Syzygy Matrix and the Differential for Rational Curves in Projective Space
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913492759478272 |
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| author | Song, Chen |
| author_facet | Song, Chen |
| contents | In this paper, we study whether a given morphism $f$ from the tangent bundle of $\mathbb{P}^1$ to a balanced vector bundle of degree $(n+1)d$ is induced by the restriction of the tangent bundle $T_{\mathbb{P}^n}$ to a rational curve of degree $d$ in $\mathbb{P}^n$. We propose a conjecture on this problem based on Mathematica computations of some examples and provide computer-assisted proof of the conjecture for certain values of $n$ and $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Syzygy Matrix and the Differential for Rational Curves in Projective Space Song, Chen Algebraic Geometry In this paper, we study whether a given morphism $f$ from the tangent bundle of $\mathbb{P}^1$ to a balanced vector bundle of degree $(n+1)d$ is induced by the restriction of the tangent bundle $T_{\mathbb{P}^n}$ to a rational curve of degree $d$ in $\mathbb{P}^n$. We propose a conjecture on this problem based on Mathematica computations of some examples and provide computer-assisted proof of the conjecture for certain values of $n$ and $d$. |
| title | The Syzygy Matrix and the Differential for Rational Curves in Projective Space |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.03985 |