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Results tagged with algebraic-curves
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user 11682
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
7
votes
Accepted
Quotient of a smooth curve by a finite group and differentials
Yes, the formula holds, even when the action is not free. Here is the principle of a proof for the case of a tame action (which covers the characteristic $0$ case). Denote by $\pi:X\to Y=X/G$ the quot …
- 4,008
5
votes
The use of embedding a curve into its Jacobian
In the section conjecture for a number field $k$: the proof of the injectivity of the map
$$X(k)\to \mathrm{HomExt}_{G_k}(G_k,\pi_1(X,\overline{x}))$$
that attributes to a rational point a section o …
- 4,008
4
votes
Does a curve over a number field have a finite etale cover of given degree
This is not a complete answer, but I am trying to translate your issue in something more tractable.
If you assume there exists a rational point $x$, then the image of the corresponding section $s=s_ …
- 4,008
7
votes
Hitchin fibration and Springer resolution
I will try to answer the first question only.
As in the remarks, the canonical reference is
Beauville, Narasimhan, Ramanan, Spectral curves and the generalised theta divisor. J. Reine Angew. Math. …
- 4,008