# 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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### Geometry of the complex Gauge group

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### Pro-representability and the obstruction to deformations of “stable curve of genus one + a section”

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### Operation on algebraic stack

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### Non-unique completion of a flat family of smooth projective varieties

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### Pullback of boundary divisors under forgetful maps

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### Flatness of the Hitchin system?

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### $\mathcal{M}_g$ and $\mathcal{A}_g$ have natural structures as quasi-projective varieties

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### Conjecture by Ekedahl on Weyl groups and Abelian varieties

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### Canonical connection on $\mathcal{A}\times X$

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### A complex analytic version of the eigencurve

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### Explicit check of the invariance of the Weyl-Petersson form

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### On the moduli stack of abelian varieties without polarization

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### Is there a precise relationship between the goals of moduli theory and the minimal model program?

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### Two components on the moduli of stable maps $\overline{\mathcal{M}}_{2,0}(\mathbb{P}^1,3)$

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### Symmetric spaces as the moduli spaces of Arakelov vector bundles

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### Moduli, Teichmüller spaces and mapping class group of a sphere with four punctures

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### Descent of projective bundles

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### Reference request: Derived structure on the moduli stack of Higgs bundles

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### Stacky proof of no elliptic curves over Z

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### The space $M_g$ with the complex structure induced from $T_g$ is a coarse moduli space for compact Riemann surfaces of genus $g$

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### Derived category of singular varieties

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### Relative logarithmic cotangent bundle

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### Presentation of $H^2(\overline{M}_{0,n},\mathbb{Z})$ as an $S_n$-module?

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### Getzler's stable graphs for modular operads

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### Riemannian metric over moduli space of Riemann spheres with n punctures

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### Unirationality of universal Jacobian over special strata of moduli space of pointed genus 3 curves

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### Explicitly computing Donaldson-Thomas invariants (of CY 3-folds)

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### vector bundles over projective line over an affine line

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### Multisections of the universal curve

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### What are the genus 4 curves with Jacobians that are 4-th powers?

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### Is the determinant map $det:\mathcal{M}(r,d)\rightarrow Pic^d(X)$ on moduli space of semistable vector bundles a fibration?

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### How did Riemann prove that the moduli space of compact Riemann surfaces of genus $g>1$ has dimension $3g-3$?

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### Eichler Shimura in higher genera

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### Rigidity of universal abelian variety

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### The fixed points set of the actions of $\mathbb{C}^*$ and $S^1$ on the Higgs bundle moduli space

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### Definition of Canonically polarized manifold?

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### Is $H^i(\mathcal{M}_g,F)$ necessarily finite dimensional for a coherent sheaf $F$?

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### Why not add cuspidal curves in the moduli space of stable curves?

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### The virtual fundamental class as derived intersection

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### Roadmap to understanding Gromov's Non-squeezing theorem

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### Image of Obstruction Map for Relative Quot-scheme

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### Nahm's equations with poles and conservation of characteristic polynomial

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### On Thurston's triangulations of sphere

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### Rationality of Eisenstein series g2 and g3 for elliptic curves defined over numberfields

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### Road map for moduli space/moduli problem/moduli stack

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### Moduli of curves over finite field

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### Total Chern Class of Hodge Bundle via CohFT

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### Stacks in moduli spaces of sheaves research

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### Purity and skyscraper sheaves

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