I'm reading $1$-forms on "Rick Miranda, Algebraic Curves and Riemann surfaces".
According to the book's notation: Let $X$ be a compact Riemann surface of genus $g$ and $\Omega^1 \left( X \right)$ be the space of holomorphic $1$-forms on $X$.
I want to prove that $\Omega^1 \left( X \right)$ has dimension $g$ over $\mathbb{C}$ as a vector space. I proved that this is a $\mathbb{C}$-vector space but I don't know how to find a basis or even a generator set $\ldots$
EDIT : I add the definition of $1$-form given by the book.