# Genus 2 curves vs Abelian surfaces

In the Satake compactification of abelian surfaces we have the following degeneration of a family of abelian surfaces in $\mathbf{H}_2$

$lim_{t \to \infty}\begin{pmatrix} it & b \\\ b & \tau\end{pmatrix} = \tau.$

Since we have that $M_2$ is an open of $A_2$, it is natural to look for a family of genus 2 curves depending on $t$ which gives the previous family of period matrices.

Can you describe explicitely such a family of genus 2 curves?

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