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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
2
votes
1
answer
250
views
Affine model of a hyperelliptic curve
We know that any hyperelliptic curve over a field with characteristic not equal to $2$ has an affine model given by $y^2 = f(x)$, with $deg(f) = 2g+1$ or $2g+2$.
Can we always find a model such that …
2
votes
0
answers
259
views
Reference for Jacobians in characteristic $p$
I am looking for a basic reference for Jacobians of algebraic curves in characteristic $p>0$. I just want basic facts about the relation between the curve and its Jacobian.
I dont want to assume fami …
3
votes
1
answer
1k
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Correspondences on curves and their induced maps on differentials?
How does a correspondence on an algebraic curve $C$ induce a map on $\Omega^1_C$? Apparently it passes through the Jacobian of $C$ but I don't quite understand it.
More specifically, I was reading a …
4
votes
3
answers
619
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Reference for hyperelliptic curves
I was reading a paper the other day that said that all automorphisms of a hyperelliptic curve are liftings of automorphisms of $\mathbb{P}^1$ operating on the set of branch points.
Can someone point …