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I'm studying Quot schemes, that I denote with $Quot_{N,X,P}$, with $N \in \mathbb{Z}$, $X \subset \mathbb{P}^d$ and $P \in \mathbb{Q}[t]$. So, I'm looking for explicit examples of Quot schemes. Could you give me as much as you can explicit examples of Quot schemes? On the net I found several papers about the construction of Quot schemes, but I can't find explicit examples in order to have a true understanding of these objects. For instance, how can I think of the Grassmannian as $Quot_{N,X,P}$ scheme? Are there different ways to do this? I'm sorry if this question isn't specific enough. Thanks in advance.

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You'll find the answer to some of your questions in N. Nitsure, Construction of Hilbert and Quot Schemes, arXiv:math/0504590.

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    $\begingroup$ Right, that's what a Google search for "explicit examples of Quot schemes" provides (and more). $\endgroup$ Nov 16, 2013 at 17:14

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