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7 votes
1 answer
305 views

An explicit negative solution to the Lüroth problem for non-algebraically closed fields

Let $\mathsf{k}$ be a field of characteristic $0$, and consider $\mathsf{k}(x,y)$. If $\mathsf{k}$ is algebraically closed, then every field $L$ such that the inclusion $\mathsf{k} \subset L \subset \...
3 votes
0 answers
149 views

Lifting of curves in characteristic zero

Let $K$ be an algebraically closed field of characteristic zero. Let $G$ be an affine reductive group over $K$, and let $H$ be a closed reductive subgroup of $G$. Since $H$ is reductive the GIT ...
1 vote
1 answer
219 views

invariants of plane quartics

Does anybody know a good reference where the invariants for plane quartic curves are developed?