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Results tagged with moduli-spaces
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user 4164
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.
10
votes
Tangent space of the stack $\overline{\mathcal{M}}_{g,n}(X,\beta)$.
The classical reference is Illusie's PhD thesis "complexe cotangent et deformations".There the result without the marked points is proven in a very, very general context using the cotangent complex; t …
- 976
6
votes
Proving that a map is a morphism
Emerton has already answered, but let me summarize all the steps:
1) to a perfect torsion complex in the derived category associate a Cartier divisor;
2) to every sequence of morphisms $C\to X\to S$ …
- 976
5
votes
There are many varieties with ample canonical bundle
If $X$ is a surface, then the Hilbert polynomial of the canonical divisor determines $d:=1-\chi(T_X)$ which is a lower bound for the dimension of any component of the moduli at the point $[X]$. Hence …
- 976