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edit approved Jan 10, 2014 at 16:08
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edit approved Jan 10, 2014 at 16:08
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Projective emebeddingembedding of curves which preserves the degree

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user43198
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Let $C$ be a projective curve (not necessarily reduced or irreducible). Let $f:C \hookrightarrow \mathbb{P}^n$ be a closed immersion. Suppose that the degree of $f(C)$ is equal to $e$. How many ways are there to embed $C$ in $\mathbb{P}^{n+1}$ such that the degree of the image is equal to $e$? Can we "parametrize" such embeddings in any way?

Let $C$ be a projective curve (not necessarily reduced or irreducible). Let $f:C \hookrightarrow \mathbb{P}^n$ be a closed immersion. Suppose that the degree of $f(C)$ is equal to $e$. How many ways are there to embed $C$ in $\mathbb{P}^{n+1}$ such that the degree of the image is equal to $e$?

Let $C$ be a projective curve (not necessarily reduced or irreducible). Let $f:C \hookrightarrow \mathbb{P}^n$ be a closed immersion. Suppose that the degree of $f(C)$ is equal to $e$. How many ways are there to embed $C$ in $\mathbb{P}^{n+1}$ such that the degree of the image is equal to $e$? Can we "parametrize" such embeddings in any way?

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user43198
user43198
  • 2k
  • 11
  • 18

Projective emebedding of curves which preserves the degree

Let $C$ be a projective curve (not necessarily reduced or irreducible). Let $f:C \hookrightarrow \mathbb{P}^n$ be a closed immersion. Suppose that the degree of $f(C)$ is equal to $e$. How many ways are there to embed $C$ in $\mathbb{P}^{n+1}$ such that the degree of the image is equal to $e$?