Which field does $\overline{\mathbb{C}(t)}$ refer to?

Question

I'm reading a textbook on algebraic geometry and it mentions the field $\overline{\mathbb{C}(t)}$ without defining it. It does define $\mathbb{C}(t)$ as the field of rational functions with coefficients in the complex numbers.

Answer 1

$\overline{\mathbb{C}(t)}$ is the algebraic closure of ${\mathbb{C}(t)}$.

For example, $\overline{\mathbb{C}(t)} $ contains an element $\tau$ such that $\tau^2-t=0,$ though $\mathbb C(t)$ does not.