I'm reading Chapter 6 of Mirror Symmetry book.
In Example 6.1.1 "A degree 3 polynomial f in $\mathbb P^2$ determines a curve of genus $g = \binom{3−1}{2} = 1$ that has the structure (induced from $\mathbb P^2$) of a complex manifold."
My question is what is genus? and why is it ${}_{3-1}C_2$ in this case?