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Results tagged with algebraic-curves
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user 4008
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
26
votes
Accepted
Which 'well-known' algebraic geometric results do not hold in characteristic 2?
I am not going to add any new examples but suggest a systematic way of looking at examples. If one looks at special phenomena in characteristic $2$ one can classify them as follows (though this divisi …
- 22.6k
14
votes
Accepted
Why is a general curve automorphism-free?
One way to do it is through deformation theory, provided we only consider
automorphism groups $G$ of order not divisible by the characteristic (one may of
course assume that it is cyclic of prime orde …
- 22.6k
13
votes
Extra automorphisms of curves and definability over \bar Q
Consider the more general case (just to lighten the notation) of a curve $X$ and
a group of automorphism $G$ (assumed to act faithfully). Consider the map $X
\rightarrow X/G$. This covering has a topo …
- 22.6k
12
votes
Accepted
Special divisors on hyperelliptic curves
Suppose that $D=x_1+x_2+\cdots+x_{g-1}$. We may assume that $\tau(x_i)\neq x_j$
for all $i\neq j$. Now, assume that $D'=y_1+\cdots+y_{g-1}$ is an element of
$|K-D|$. Then $x_1+x_2+\cdots+x_{g-1}+y_1+\ …
- 22.6k