Let the complex form $z_{1}+dz_{1}\wedge dz_{2}$ on $D^{2}\times T^{2}$ ,where $D^2$ is a unit disk un $z_{1}$-plane. here $z_{1}$ and $z_{2}$ is a standard coordinates on $\mathbb{C^2}$. I read on paper that on $z_{1}=0$ the complex structure is smooth elliptic curve with Teichmüller parameter $τ=i$.
Can you simple description to “smooth elliptic curve with Teichmüller parameter $τ=i$”?
I have introduction knowledge about complex geometry ie, if you describe it with standard complex coordinates, with standard 1-form or integrable complex structure , I understand very easily.