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Given an ideal $I \subset \mathbb{C}[x,y]$ such that $\text{dim}_{\mathbb{C}}\mathbb{C}[x,y]/I = n$, can the dimension of the space $Hom_{\mathbb{C}[x,y]}(I , \mathbb{C}[x,y]/ I)$ be determined in some elementary way?

$\text{dim}_{\mathbb{C}}Hom_{\mathbb{C}[x,y]}(I , \mathbb{C}[x,y]/ I)$

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    I doubt whether there is any easy way to calculate it. – 2017-01-30

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