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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$\begingroup$ Would some of the links provided by a Google search for "explicit examples of Quot schemes" be useful? (It's not my specialization). $\endgroup$– Włodzimierz HolsztyńskiNov 16, 2013 at 16:19
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$\begingroup$ @WlodzimierzHolsztynski I'm sorry, but unfortunately I can't find them! $\endgroup$– Oscar1778Nov 16, 2013 at 16:40
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$\begingroup$ msp.org/pjm/2007/231-2/pjm-v231-n2-p07-s.pdf: "...explicit...of quot schemes..." by Gustavsen at al $\endgroup$– Włodzimierz HolsztyńskiNov 16, 2013 at 17:06
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$\begingroup$ algant.eu/documents/theses/habibi.pdf: "Hilbert and Quot Schemes" by S.Habibi $\endgroup$– Włodzimierz HolsztyńskiNov 16, 2013 at 17:10
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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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1$\begingroup$ Right, that's what a Google search for "explicit examples of Quot schemes" provides (and more). $\endgroup$ Nov 16, 2013 at 17:14