Quadratic Varieties of Small Codimension
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913894231965696 |
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| author | Watanabe, Kiwamu |
| author_facet | Watanabe, Kiwamu |
| contents | Let $X \subset \mathbb{P}^{n+c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that $X$ is a complete intersection provided that $n \geq 2c+1$. As the extremal case, they also classified $X$ with $n=2c$. In this paper, we classify $X$ with $n=2c-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic Varieties of Small Codimension Watanabe, Kiwamu Algebraic Geometry Complex Variables Differential Geometry 14J40, 14J45, 14M10, 14M17, 51N35 Let $X \subset \mathbb{P}^{n+c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that $X$ is a complete intersection provided that $n \geq 2c+1$. As the extremal case, they also classified $X$ with $n=2c$. In this paper, we classify $X$ with $n=2c-1$. |
| title | Quadratic Varieties of Small Codimension |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14J40, 14J45, 14M10, 14M17, 51N35 |
| url | https://arxiv.org/abs/2405.04002 |