# Questions tagged [moduli-space]

A Moduli space is a space in algebraic geometry whose points are geometric objects or isomorphism classes of these kinds of objects.

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### Family of vector spaces over a scheme

In Example 2.12 of the notes by Victoria Hoskins, the concept of a naive moduli problem is introduced, focusing on vector bundles (locally free sheaves) on a fixed scheme ( X ) up to isomorphism. The ...
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### Moduli spaces of surfaces to algebraic stacks

I've been reading through Farb and Margalit's book on the action of the mapping class group on Teichmuller space to get a moduli space. This is a very topological/geometric construction, looking at ...
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### Find the center of all circles that touch the $x$-axis and a circle centered at the origin

Given a circle $C$ of radius $1$ centered at the origin, I want to determine the locus of the centers of all circles that touch $C$ and the $x$-axis. This is the red curve in the following Desmos ...
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### Elementary question about the definition of moduli space $\mathcal{M}_{g,n}$.

I watched wikipedia page Moduli space, and the definition of $n$-marked moduli space as follow One can also enrich the problem by considering the moduli stack of genus $g$ nodal curves with $n$ ...
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### Stability of vector bundles as GIT quotient

I believe that the stability of vector bundles or coherent sheaves (defined as the inequality of 'slopes' of its subsheaves) comes naturally from GIT. However, in any literature I can find, it is ...
• 81
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### Zariski tangent space to a moduli space

I’m reading the paper 13/2 Ways of Counting Curves by Pandharipande and Thomas. I’m very confused with the following statement on page 8 $\S$ Deformation theory. We return now to the deformation ...
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### Euler-Poincaré formula for foliations

Does someone have a nice proof for Proposition 11.14 in Farb&Margalits "Primer to Mapping Class Groups", which states the following: Let $S$ be a closed surface with a singular foliation ...
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