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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
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
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