Consider the canonical line bundle $K_C$ for $C$ defined by the compactification of $f=y^3-x^5+1$. $K_C$ is the as a set the set of holomorphic $1$-forms on $C$. How does one go about finding the basis for $K_C$?
I have seen an example for hyperellptic curves that gives the basis as $z^adz/w$, where $w$ is the product of rational functions having divisors precisely at ramification points and infinity. This does not even seem holomorphic to me, and I am thus confused in general.