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Sasha
Sasha
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Let $X\subset \mathbb CP^n$ be a smooth submanifold whose normal bundle is $$\sum_{i=1}^{codim X}=O(k_i).$$$$\bigoplus_{i=1}^{codim X}O(k_i).$$

Is there some general enough additional condition of $X$ that implies that $X$ is a complete intersection? For example, would $dimX\ge 2$ suffice (to exclude things like $X=\mathbb CP^1$)?

Let $X\subset \mathbb CP^n$ be a smooth submanifold whose normal bundle is $$\sum_{i=1}^{codim X}=O(k_i).$$

Is there some general enough additional condition of $X$ that implies that $X$ is a complete intersection? For example, would $dimX\ge 2$ suffice (to exclude things like $X=\mathbb CP^1$)?

Let $X\subset \mathbb CP^n$ be a smooth submanifold whose normal bundle is $$\bigoplus_{i=1}^{codim X}O(k_i).$$

Is there some general enough additional condition of $X$ that implies that $X$ is a complete intersection? For example, would $dimX\ge 2$ suffice (to exclude things like $X=\mathbb CP^1$)?

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aglearner
aglearner
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Projective submanifolds of $\mathbb CP^n$ whose normals bundles are sums of linear.

Let $X\subset \mathbb CP^n$ be a smooth submanifold whose normal bundle is $$\sum_{i=1}^{codim X}=O(k_i).$$

Is there some general enough additional condition of $X$ that implies that $X$ is a complete intersection? For example, would $dimX\ge 2$ suffice (to exclude things like $X=\mathbb CP^1$)?