Interpolation for degree 2 Veroneses of odd dimension
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910713713262592 |
|---|---|
| author | Shang, Ray |
| author_facet | Shang, Ray |
| contents | A classical fact is that through any $d+3$ general points in $\mathbb{P}_\mathbb{C}^d$ there exists a unique rational normal curve of degree $d$ passing through them. We generalize this by proving the following: when $n$ is odd, for any $\binom{n+2}{2} + n+1$ general points in $\mathbb{P}_\mathbb{C}^{\binom{n+2}{2} - 1}$, there exist at least $2^{n(n-1)}$ degree 2 Veroneses passing through them. This makes substantial progress on a question of Aaron Landesman and Anand Patel, and extends the work of Arthur Coble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolation for degree 2 Veroneses of odd dimension Shang, Ray Algebraic Geometry A classical fact is that through any $d+3$ general points in $\mathbb{P}_\mathbb{C}^d$ there exists a unique rational normal curve of degree $d$ passing through them. We generalize this by proving the following: when $n$ is odd, for any $\binom{n+2}{2} + n+1$ general points in $\mathbb{P}_\mathbb{C}^{\binom{n+2}{2} - 1}$, there exist at least $2^{n(n-1)}$ degree 2 Veroneses passing through them. This makes substantial progress on a question of Aaron Landesman and Anand Patel, and extends the work of Arthur Coble. |
| title | Interpolation for degree 2 Veroneses of odd dimension |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.16672 |