# Questions tagged [moduli-spaces]

Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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### Mapping Class Group and Triangulations

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### Moduli space of flat connections of Lie group over a 2-torus

**10**

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### Moduli space of curves

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### SL(2,R) invariant which are not SL(2,C) invariants

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### Decorated Teichmuller space of a punctured disk and moduli space of the annuls

**4**

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### A website which explains Mazur's torsion point theorem

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### Local factoriality of moduli space of semistable G-Higgs bundles on curve

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### The Deligne-Mumford Compactification for Closed Surfaces

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### Prerequisites for reading papers of arithmetic such as Ribet, Mazur, Faltings, Wiles

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### Is a Procesi bundle equipped with a hyperholomorphic connection?

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### Moduli space is a Calabi-Yau manifold?

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### The construction of moduli space of stable maps

**7**

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### The Precise Meaning of the Moduli Space of Flat Connections?

**3**

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### Derived functor giving algebraic map between moduli

**0**

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### How to construct $ \mathcal{H} ( \mathbb{P}^n ) = \{ \ \text{Smooth projective subvarieties of } \mathbb{P}^n \ \} $?

**7**

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### Maps between moduli of curves

**2**

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### Is the stack of stable curves with no rational component algebraic?

**13**

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### Moduli space of linear partial differential equations

**10**

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### Good introductory references on moduli (stacks), for arithmetic objects

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### How to calculate : $ \mathrm{Hdg}^{ 2 \bullet } ( \mathcal{H}\mathrm{ilb} ( \mathbb{P}^n ),\mathbb{Q} ) $?

**4**

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### The ¨irreducible¨ representation variety of surface group

**4**

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### Confusion in known result about Moduli space of vector bundle of rank 2 degree 0 vector bundles over smooth curve of genus 2

**7**

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### What are some open problems in moduli spaces and moduli stacks?

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### Computing $H^*(BDiff(W_{\infty},D^{\infty});\mathbb{Q})$ via Mumford-Morita-Miller classes

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### Generalizing the Madsen-Weiss Theorem via the scanning map $\mathscr{C}(M,\mathbb{R}^{\infty})\to\Omega^{\infty}AG^+_{\infty,d}$

**4**

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### Virtual fundamental class of Moduli space of stable maps in genus 1

**7**

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### Is a torsion free sheave of rank one on a reducible curve the pushforward of a line bundle on a normalization?

**8**

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### Moduli interpretation of Fargues-Fontaine curve

**3**

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### Stable torsion free sheaf on smooth projective surface

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### When is the moduli of generalized parabolic bundles with fixed determinant smooth?

**6**

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### Rationality of the moduli space of genus g curves

**8**

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### Moduli 'space' of stacks?

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### Moduli of stable and semistable $G$-Higgs bundles on curves

**2**

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### Tangent and cotangent bundle of a smooth algebraic stack

**2**

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### How to split a Multi-section into finitely many Sections via base-change?

**2**

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### Metric on moduli space of semistable principal G-bundles on curves

**2**

**1**answer

### Moduli problem of stable nodal curves over the integers

**4**

**2**answers

### Generic Mumford Tate group and algebraic points

**8**

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### Genus=2 theta functions, Arnold's relation, and KZ connection

**7**

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### Galois representations associated to the modular tower and automorphy

**8**

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### Fundamental group of moduli space of K3's

**4**

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### On a presentation of $\bar{M}_{2,1}$

**5**

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### A log structure on the moduli space of curves

**3**

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### determinant of a coherent sheaf, locally free on a big open set

**15**

**2**answers

### Is a cubic hypersurface determined by its Fano variety of lines?

**4**

**1**answer

### moduli stack of double covers of $\mathbb{P}^1$ with one marked point

**3**

**1**answer

### Isomorphism classes of line bundles with connections

**2**

**1**answer

### Build a Fuchsian group starting from punctures on a disk

**1**

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### Cutting a circle from the hyperbolic plane

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**1**answer