# Tagged Questions

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**1**answer

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### Is Mumford's statement about the representability of some functor wrong?

I am having trouble proving a result in Mumfords book 'Lectures on Curves on an Algebraic surface.
It is a statement about the representability of some functor. It is stated on page 108 and says the ...

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755 views

### Relationship between Hilbert schemes and deformation spaces

Hi, I'm just starting to learn about deformation theory (via Hartshorne's Deformation theory, as well as Fantechi's section of FGA explained), and I feel like I'm confused about fundamental concepts. ...

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### Why is Maps(X,Y) an open subfunctor of Hilb(X x Y)?

Let $X$ and $Y$ be projective schemes. Then we can define the mapping scheme between them, $\rm{Maps}(X,Y)$ as follows:
To any map $f:X\rightarrow Y$ we consider the graph $\Gamma_f$ as a closed ...