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Results tagged with moduli-spaces
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user 1784
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.
7
votes
Moduli space of K3 surfaces
Why aren't you happy with the moduli space of polarized K3's, i.e. pairs $(X,L)$ where $L$ is an ample line bundle? This is standard, and this at least makes sense over any field or $\mathbb Z$. And t …
- 13.1k
24
votes
Accepted
Is the Torelli map an immersion?
Respectfully, I disagree with Tony's answer. The infinitesimal Torelli problem fails for $g>2$ at the points of $M_g$ corresponding to the hyperelliptic curves. And in general the situation is trickie …
- 13.1k
12
votes
What is the Euler characteristic of a Hilbert scheme of points of a singular algebraic curve?
The same formula holds for $\chi(X^{[n]})$ of any topological space for which $\chi(X)$ is defined and behaves in the expected way for unions, Cartesian products, and quotients by a finite free action …
- 13.1k