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Results tagged with moduli-spaces
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user 439
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.
16
votes
Accepted
Moduli space of flat bundles
You have to be a bit careful here. Over $\mathbb{C}$ the stack of representations of $\pi_{1}(X)$ in $G$ and the stack of flat algebraic $G$-bundles on $X$ are isomorphic as complex analytic stacks b …
- 6,239
9
votes
Accepted
Moduli spaces of coherent sheaves on K3s
This follows from a result of Yoshioka. In Theorem 8.1 of this paper Yoshioka showed that every moduli space of coherent sheaves on a K3 surface $X$ is deformation equivalent to an appropriate Hilbert …
- 6,239
11
votes
Is the Torelli map an immersion?
Yes the Torelli map is an immersion, at least over $\mathbb{C}$. The Torelli theorem says that the map separates points (on the stack level it also says tha the map is representable) and the infinites …
- 6,239
4
votes
Reference for the Hodge Bundle
The list of references is way too long. Here are some classical texts containing both the setup and calculations:
1) P. Deligne, Le déterminant de la cohomologie, Current Trends in Arithmetical Algeb …
- 6,239
7
votes
Gromov-Witten theory and compactifications of the moduli of curves
Here is a random thought on the second part of Kevin's question. There are various compactifications of the space of maps that should be meaningful physically but haven't been explored by the physicis …
- 6,239