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Results tagged with moduli-spaces
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user 7108
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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A log structure on the moduli space of curves
Let $M_{g, n}$ be the moduli space of curves of genus $g$ with $n$ marked points. Let $M_{g, \vec{n}}$ be the moduli space of marked curves with a choice of a (possibly zero) tangent vector at each ma …
- 7,952
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votes
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answer
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Moduli problem of stable nodal curves over the integers
Over an algebraically closed field of characteristic zero, e.g. $\overline{\mathbb{Q}}$, the Deligne-Mumford stack $\overline{\mathcal{M}}_{g,n}$ represents the functor $$\overline{\mathcal{M}}_{g,n}( …
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Accepted
Derived category of singular varieties
Let $\tilde{X}_k$ be the normalization of the closed $k$-codimension stratum, so $\tilde{X}_0$ is the normalization of $X$. Then there is a diagram of pullback functors between the categories $\text{P …
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The virtual fundamental class as derived intersection
Say $X$ is a smooth projective variety and $\beta\in H_2(X)$ is a class. Then there is a finite-type proper scheme (or in general, stack) $SM : = \overline{\mathcal{M}}_{g,n}(X,\beta)$ of stable maps …
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