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Results tagged with algebraic-curves
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user 94086
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
4
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0
answers
244
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Why does the Galois twist of this cover specialize to a certain field extension?
I didn't feel MO was the best place to ask this question, so apologies for this, but when I asked it at https://math.stackexchange.com/questions/2297837/why-is-this-cubic-polynomial-generic-for-cyclic …
- 1,142
4
votes
1
answer
216
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Does a smooth relative curve $X/S$ embed into $\mathbb{P}^3_S$?
Suppose that $\pi:X\to S$ is a smooth projective morphism of relative dimension 1. If $S$ is the spectrum of an algebraically closed field, then it is known that $X$ embeds into $\mathbb{P}^3_S$.
Ques …
- 1,142
2
votes
0
answers
175
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vanishing of higher algebraic de Rham cohomology and sheaves of differentials for singular c...
I'm looking for some results or references about de Rham cohomology of curves in less-than-optimal cases. The two vanishing results I care about are:
$H^{k}_{\text{dR}}(X) = 0$ for $k>2$, since $H^{ …
- 1,142