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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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+\ …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar