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arXiv · 2405.04002

Quadratic Varieties of Small Codimension

Kiwamu Watanabe
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Abstract

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 $n=2c-1$.

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Kiwamu Watanabe. 2024-05-07. Quadratic Varieties of Small Codimension. https://doi.org/10.3842/sigma.2025.045

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