3 problems

Let $X$ be a hyperelliptic curve over a field of characteristic $0$, and let $K_X$ denote its field of moduli. The automorphism group of $X$ is denoted by $\operatorname{Aut}(X)$.…

Real rational-map conjecture. Every real rational map is definable over its field of moduli.

Let $D$ be a dessin described by permutations $a,b$, and let $G$ be its monodromy group. Define … Let the field of moduli of $D$ be the fixed field of its stabilizer in…