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Results tagged with algebraic-curves
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user 1784
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
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
12
votes
Accepted
Smoothness of Symmetric Powers
Just convince yourself that if $(C,P_1,\dots,P_n)$ and $(D,Q_1,\dots,D_n)$ are analytically isomorphic -- $C$ at the point $P_i$, $D$ at the point $Q_i$ -- then $Sym^n C$ at the point $(P_1,\dots,P_n) …
- 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