%0 Journal Article
%T An effective proof of the hyperelliptic Shafarevich conjecture
%A Rafael von K£¿nel
%J Mathematics
%D 2013
%I arXiv
%X Let $C$ be a hyperelliptic curve of genus $g\geq 1$ over a number field $K$ with good reduction outside a finite set of places $S$ of $K$. We prove that $C$ has a Weierstrass model over the ring of integers of $K$ with height effectively bounded only in terms of $g$, $S$ and $K$. In particular, we obtain that for any given number field $K$, finite set of places $S$ of $K$ and integer $g\geq 1$ one can in principle determine the set of $K$-isomorphism classes of hyperelliptic curves over $K$ of genus $g$ with good reduction outside $S$.
%U http://arxiv.org/abs/1310.6727v1