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Results tagged with algebraic-curves
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user 605
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
4
votes
Extending maps of curves
I don't think you can extend an arbitrary morphism, even if the curves are prestable.
For instance, if $C_0$ is a quartic with one node and the generic element is a smooth quartic then
you do have …
- 8,828
3
votes
Smoothness of Symmetric Powers
Edit: It seems appropriate to recall here Chevalley-Shephard-Todd's Theorem.
It says the quotient of $\mathbb A^n_k$ by a finite linear group $G$ with order prime to the characteristic of $k$ is smoo …
- 8,828
7
votes
Accepted
Curves with negative self intersection in the product of two curves
Disclaimer. The answer below is a variation of Bogomolov's argument and it would not come to be without Dmitri's answer. If you feel like upvoting this, please upvote his answer.
Curves on products …
- 8,828