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?**