Curves of genus two covering elliptic curves, by Tony Shaska

This paper has now been accepted by the Journal of Symbolic Computation under the title "Curves of genus 2 with (N,N) decomposable Jacobians". At the author's request, the preprint has been removed. The following is an abstract of the paper. \begin{abstract} Let $C$ be a curve of genus 2 and $\psi_1:C \to E_1$ a map of degree $n$, from $C$ to an elliptic curve $E_1$. This map induces a degree $n$ map $\phi_1:\bP^1 \to \bP^1$ which we call a Frey-Kani covering. We determine all possible ramifications for $\phi_1$. If $\psi_1:C \to E_1$ is maximal then there exists a maximal map $\psi_2:C\to E_2$, of degree $n$, to some elliptic curve $E_2$. If the degree $n$ is odd the pair $(\psi_2, E_2)$ is canonically determined. For $n=3$ we determine explicitly $\phi_2:\bP^1\to \bP^1$ in terms of $\phi_1$ and find an algebraic description of the moduli space parameterizing Frey-Kani coverings of degree 3. \end{abstract}

Tony Shaska <tts@math.ufl.edu>