Holomorphic cubic differential ($c\in H^0(X,K_X^3)$)

A section of the cube of the canonical bundle, locally $c=\varphi (z)d{z}^3$ with holomorphic coefficient. The flat coordinates obtained by integrating cube roots have transitions $w\mapsto \zeta w+b$, ${\zeta }^3=1$; general real-linear deformations do not preserve these as holomorphic transitions.