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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On the dimension of moduli space of pointed curves with fixed Weierstrass semigroup
Does anyone know any information on the question of the dimension of moduli space of pointed curves with fixed Weierstrass semigroup? Some conjecture?
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Intuition behind moduli space of curves
For a genus g compact smooth surface $M$, an algebraic structure is the same as a complex structure is the same as a conformal structure. So the moduli space of smooth curves should be the same as the ...
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Are Jacobians principally polarized over non-algebraically closed fields?
How does one define the Torelli map $M_g \to A_g$ of moduli stacks? On geometric points a curve maps to its principally polarized Jacobian.
So what I am asking is: if I have a curve $C$ over a non-...
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Moduli space of flat bundles
Is there a good place to learn about the structure of moduli stack of flat $G$-bundles on an algebraic curve?
Of course, we're just studying representations of a group $\pi_1(X)\to G$ modulo some ...
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Exotic automorphisms of the fundamental group of a curve?
A while back, Jordan S. Ellenberg brought the following problem to my attention.
If $G$ is a residually finite group, let $\widehat G$ be its profinite completion.
Let $S$ be a closed surface of ...
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"A theory of generalized Donaldson-Thomas invariants" by Joyce & Song
Is anyone else working through this paper: A theory of generalized Donaldson-Thomas invariants, by Dominic Joyce, Yinan Song? I am trying to verifying example 6.2 (m=2 for simplicity) using only the ...
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How does one intersect non-transverse divisors on Mg-bar.
Let Mg-bar be the Deligne-Mumford compactification of genus g curves, and let δ1 be the divisor of degenerate curves of the form `genus 1 meeting a genus g-1 transversely".
Question 1: What ...
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Line bundles on moduli spaces
This is perhaps too broad or vague (or silly) a question, but here it is anyway: why should I care about constructing line bundles on a moduli space? This comes up all of the time, but I seem to be ...
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Why is the Hodge class of \bar{M_g} big and nef?
Let pi: \bar{Mg,1} \to \bar{M_g} be natural projection of compactified moduli stacks of curves and let omega be the relative dualizing sheaf. Then the Hodge class \lambda of \bar{M_g} is the first ...
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Kodaira-Spencer Theory and moduli of curves
I was looking at a paper of Farkas and the following confusing point came up.
Let $\mathscr{M}_g$ be the moduli stack of smooth genus $g$ curves and let $\pi: \mathscr{C} \to \mathscr{M}_g$ be the ...
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Moduli spaces of complex curves as algebraic varieties
Using a minimum of technical vocabulary, give a summary of why it is that the moduli space of genus g complex curves with n marked points has a natural compactification that is isomorphic (as a ...
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Gromov-Witten theory and compactifications of the moduli of curves
Why, from a string theory perspective, is it natural to consider the Deligne-Mumford (resp. Kontsevich) compactification of the moduli of curves (resp. maps [from curves to a target space X]) rather ...
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Geometric calculations using Grassmann variables
Physicists seem to get huge computational value by introducing Grassmann variables and Grassmann integration into differential geometric calculations.
See: http://en.wikipedia.org/wiki/...
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Algorithms for semistable reduction of families of curves
This is a somewhat vague question which came up MSRI a few days ago: Suppose I have a family of curves over a one dimensional base, given in a computationally explicit way. For example, maybe I have a ...
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cohomology of moduli spaces
Does anyone know if there's any reference on the $\ell$-adic cohomology of some simple moduli spaces/Shimura varieties, like Siegel moduli varieties $A_{g,N}$ of genus $g$ and level $N,$ for small $g$ ...
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What is the affinization of M_g?
This question is inspired by What is an example of a function on M_g? . Consider Mg, the moduli space of genus g curves, NOT compactified. When g is 3 or greater, this is not affine. Does anyone know ...
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What is an example of a function on M_g?
It feels bad talking about a space without knowing a single function on it, hah?
So what is a function on the moduli space of curves, from the geometric point of view?
From the functorial point of ...
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Dualizing sheaf on singular curves
I am trying to understand the stabilization map, which takes a prestable curve (a curve with some marked points, and at worst nodal singularities) and returns a stable curve (a curve with some marked ...
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Why and how are moduli spaces of (semi)stable vector bundles well-behaved?
The slope of a vector bundle $E$ is defined as $\mu(E) = \deg(E)/\mathrm{rank}(E)$. Then a vector bundle $E$ is called semistable if $\mu(E') \leqslant \mu(E)$ for all proper sub-bundles $E'$. It is ...
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Ribbon graph decomposition of the moduli space of curves
What is a ribbon graph? What is the ribbon graph decomposition of the moduli space of curves? What are some good references for this material?
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